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### Is zero even or odd?

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```I know 0 is neither negative or positive but what about odd/even? I think
it's even.

Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
```
 0
Reply gactimus (1330) 12/20/2004 2:21:11 PM

See related articles to this posting

```Gactimus wrote:
> I know 0 is neither negative or positive but what about odd/even? I thi=
nk
> it's even.=20
>=20
> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

As it can be divided by 2 without a remainder, it is obviously even.

--=20
Josef M=F6llers (Pinguinpfleger bei FSC)
If failure had no penalty success would not be a prize
-- T.  Pratchett

```
 0
Reply Josef 12/20/2004 2:24:39 PM

```Josef Moellers wrote:
>
> Gactimus wrote:
> > I know 0 is neither negative or positive but what about odd/even? I think
> > it's even.
> >
> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>
> As it can be divided by 2 without a remainder, it is obviously even.

The divisor would have to be something smaller than 0 like -2.
Therefore zero is both even and negative.

>
> --
> Josef M�llers (Pinguinpfleger bei FSC)
>         If failure had no penalty success would not be a prize
>                                                 -- T.  Pratchett

```
 0
Reply BB 12/20/2004 2:34:03 PM

```>>>>> "BB" == BB  <BB@BB.BB> writes:

BB> The divisor would have to be something smaller than 0 like -2.
BB> Therefore zero is both even and negative.

This is a troll.   *Negative*?  Can I have some of the drug you're
smoking? :)

--
Randal L. Schwartz - Stonehenge Consulting Services, Inc. - +1 503 777 0095
<merlyn@stonehenge.com> <URL:http://www.stonehenge.com/merlyn/>
Perl/Unix/security consulting, Technical writing, Comedy, etc. etc.
See PerlTraining.Stonehenge.com for onsite and open-enrollment Perl training!
```
 0
Reply merlyn 12/20/2004 3:02:45 PM

```On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:

>Josef Moellers wrote:
>>
>> Gactimus wrote:
>> > I know 0 is neither negative or positive but what about odd/even? I think
>> > it's even.
>> >
>> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> As it can be divided by 2 without a remainder, it is obviously even.
>
>The divisor would have to be something smaller than 0 like -2.
>Therefore zero is both even and negative.

---
Zero has no sign. Consider:

If zero was positive, 1+0 > 1, but 1+0 = 0
If zero was negative, 1+0 < 1, but 1+0 = 0

--
John Fields
```
 0
Reply John 12/20/2004 3:13:35 PM

```On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:

>Josef Moellers wrote:
>>
>> Gactimus wrote:
>> > I know 0 is neither negative or positive but what about odd/even? I think
>> > it's even.
>> >
>> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> As it can be divided by 2 without a remainder, it is obviously even.
>
>The divisor would have to be something smaller than 0 like -2.

Huh? 0/2 is somehow undefined because 2 > 0? Interesting.

>Therefore zero is both even and negative.
>
>>
>> --
>> Josef M�llers (Pinguinpfleger bei FSC)
>>         If failure had no penalty success would not be a prize
>>                                                 -- T.  Pratchett
>

************************

David C. Ullrich
```
 0
Reply David 12/20/2004 3:19:39 PM

```Randal L. Schwartz wrote:
>>>>>>"BB" == BB  <BB@BB.BB> writes:
>>>>>
>
> BB> The divisor would have to be something smaller than 0 like -2.
> BB> Therefore zero is both even and negative.
>
> This is a troll.   *Negative*?  Can I have some of the drug you're
> smoking? :)
>

It's not a prime, because a prime can
only be divided by itself and 1.
0 can't be divided by itself, but
can be divided by everything else.
An anti-prime?
John

```
 0
Reply John 12/20/2004 3:21:25 PM

```"BB" <BB@BB.BB> wrote in message news:10sdomrcqe6qt0e@corp.supernews.com...
> Josef Moellers wrote:
>>
>> Gactimus wrote:
>> > I know 0 is neither negative or positive but what about odd/even? I
>> > think
>> > it's even.
>> >
>> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> As it can be divided by 2 without a remainder, it is obviously even.
>
> The divisor would have to be something smaller than 0 like -2.
> Therefore zero is both even and negative.
>
>>
>> --
>> Josef M�llers (Pinguinpfleger bei FSC)
>>         If failure had no penalty success would not be a prize
>>                                                 -- T.  Pratchett
>
>
I seeem to recall 0 coming up negative in some old IBM mainframes. That was
an artifact of the way signed numbers were converted to binary.

Tam

```
 0
Reply Tam 12/20/2004 3:30:30 PM

```"John Sefton" <john@petcom.com> wrote

> 0 can't be divided by itself,

Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1

It works if the only three numbers in the universe are
0, 1, and infinity -- A number system that seems very
suited to usenet.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/20/2004 3:36:15 PM

```Randal L. Schwartz wrote:
>>>>>>"BB" == BB  <BB@BB.BB> writes:
>
>
> BB> The divisor would have to be something smaller than 0 like -2.
> BB> Therefore zero is both even and negative.
>
> This is a troll.   *Negative*?  Can I have some of the drug you're
> smoking? :)

Well, it's called "negative" in French. (also positive, in order to
be logically consistent). And their bridges hold up pretty well.

as to the antecedent, woo hoo! I'd guess sleep deprivation.

--
Mitch Harris
(remove q to reply)

```
 0
Reply Mitch 12/20/2004 3:38:38 PM

```I read in sci.electronics.design that Gactimus <gactimus@xrs.net> wrote
(in <10sdnunotbnere2@corp.supernews.com>) about 'Is zero even or odd?',
on Mon, 20 Dec 2004:
>I know 0 is neither negative or positive but what about odd/even? I think
>it's even.
>
>Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

There is other evidence. Even powers of negative numbers are positive,
and (-x)^0 = 1, which is usually positive. (;-)
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/20/2004 3:40:38 PM

```In article <41C6EDF5.1050205@petcom.com>, John Sefton  <john@petcom.com> wrote:

>It's not a prime, because a prime can
>only be divided by itself and 1.

If you rephrase that as "is a multiple only of 1 and itself" you will save
yourself the exception

>0 can't be divided by itself

-- Richard
```
 0
Reply richard 12/20/2004 3:42:24 PM

```> > > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> > > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
> >
> > As it can be divided by 2 without a remainder, it is obviously even.
>
> The divisor would have to be something smaller than 0 like -2.
> Therefore zero is both even and negative.
>

A number n is considered even if there exists an integer m such that n = 2m.
Since 0 = (2) (0), it is even.

However, zero is *not* negative, or positive for that matter.  Positive and
negative numbers are defined in terms of 0, with positive being > 0 and
negative being < 0.  Since 0 is not greater than 0 and 0 is not less than 0,
0 is not positive or negative.

Just for kicks, zero is a *non-negative* and *non-positive* number, since
both of these sets include 0.

```
 0
Reply Richards 12/20/2004 3:47:57 PM

```I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
'Is zero even or odd?', on Mon, 20 Dec 2004:

>"John Sefton" <john@petcom.com> wrote
>
>> 0 can't be divided by itself,
>
>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1

One possible solution, given the enormous lack of rigour in 'infinity'.
But in general, 0/0 can take any value. Consider:

Lim {@->0}[(2377.pi.sin@)/@] = 2377.pi

--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/20/2004 3:48:23 PM

```"John Fields" <jfields@austininstruments.com> wrote in message
news:anqds054e36bfqtm3m7s15n3kk0o2r37jk@4ax.com...
> On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>
>>Josef Moellers wrote:
>>>
>>> Gactimus wrote:
>>> > I know 0 is neither negative or positive but what about odd/even?
>>> > I think
>>> > it's even.
>>> >
>>> > Odd numbers start at 1 and go every other number
>>> > 1,3,5,7;1,-1,-3,-5,-7
>>> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>>
>>> As it can be divided by 2 without a remainder, it is obviously even.
>>
>>The divisor would have to be something smaller than 0 like -2.
>>Therefore zero is both even and negative.
>
> ---
> Zero has no sign. Consider:
>
> If zero was positive, 1+0 > 1, but 1+0 = 0
> If zero was negative, 1+0 < 1, but 1+0 = 0

I thought 1+0 = 1, but I guess I can't do hard sums.
Androcles.

> --
> John Fields

```
 0
Reply Androcles 12/20/2004 3:50:04 PM

```> I seeem to recall 0 coming up negative in some old IBM mainframes. That was
> an artifact of the way signed numbers were converted to binary.

In computers using ones complement arithmetic, the number zero can be
represented in two ways: all bits zero (which appears positive) or all
bits one (which appears negative).

But this is just a matter of how numbers are represented in the machine,
and says nothing about whether zero is really a positive number, a
negative number, or neither.m

--
Alec McKenzie
mckenzie@despammed.com
```
 0
Reply Alec 12/20/2004 4:02:50 PM

```On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:

>Josef Moellers wrote:
>>
>> Gactimus wrote:
>> > I know 0 is neither negative or positive but what about odd/even? I think
>> > it's even.
>> >
>> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> As it can be divided by 2 without a remainder, it is obviously even.
>
>The divisor would have to be something smaller than 0 like -2.
>Therefore zero is both even and negative.
>
>>
>> --
>> Josef M�llers (Pinguinpfleger bei FSC)
>>         If failure had no penalty success would not be a prize
>>                                                 -- T.  Pratchett
>

PSpice uses...

�          +1 if x>0
�SGN(x) =   0 if x=0
�          -1 if x<0

which matches up with what is shown on Wolfram's site...

http://mathworld.wolfram.com/Sign.html

A real royal nuisance when applying SGN(x) to system behavioral
modeling.

...Jim Thompson
--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |

I love to cook with wine.      Sometimes I even put it in the food.
```
 0
Reply Jim 12/20/2004 4:07:37 PM

```BB <BB@BB.BB> wrote in message news:10sdomrcqe6qt0e@corp.supernews.com:

> Josef Moellers wrote:
>>
>> Gactimus wrote:
>> > I know 0 is neither negative or positive but what about odd/even? I
>> > think it's even.
>> >
>> > Odd numbers start at 1 and go every other number
>> > 1,3,5,7;1,-1,-3,-5,-7 Even starts at 2 and go every other number
>> > 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> As it can be divided by 2 without a remainder, it is obviously even.
>
> The divisor would have to be something smaller than 0 like -2.
> Therefore zero is both even and negative.

Really? Is [positive number]*0 negative?

>>
>> --
>> Josef M�llers (Pinguinpfleger bei FSC)
>>         If failure had no penalty success would not be a prize
>>                                                 -- T.  Pratchett
>
>

```
 0
Reply Mr 12/20/2004 4:16:41 PM

```"BB" <BB@BB.BB> wrote in message
news:10sdomrcqe6qt0e@corp.supernews.com...
> Josef Moellers wrote:
> >
> > Gactimus wrote:
> > > I know 0 is neither negative or positive but what about
odd/even? I think
> > > it's even.
> > >
> > > Odd numbers start at 1 and go every other number
1,3,5,7;1,-1,-3,-5,-7
> > > Even starts at 2 and go every other number
2,4,6,8;2,0,-2,-4,-6,-8
> >
> > As it can be divided by 2 without a remainder, it is obviously
even.
>
> The divisor would have to be something smaller than 0 like -2.
> Therefore zero is both even and negative.

Oh, dear.

Franz

```
 0
Reply Franz 12/20/2004 4:24:42 PM

```"Tam/WB2TT" <t-tammaru@c0mca\$t.net> wrote in message
>
> "BB" <BB@BB.BB> wrote in message
> news:10sdomrcqe6qt0e@corp.supernews.com...
>> Josef Moellers wrote:
>>>
>>> Gactimus wrote:
>>> > I know 0 is neither negative or positive but what about odd/even?
>>> > I think
>>> > it's even.
>>> >
>>> > Odd numbers start at 1 and go every other number
>>> > 1,3,5,7;1,-1,-3,-5,-7
>>> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>>
>>> As it can be divided by 2 without a remainder, it is obviously even.
>>
>> The divisor would have to be something smaller than 0 like -2.
>> Therefore zero is both even and negative.
>>
>>>
>>> --
>>> Josef M�llers (Pinguinpfleger bei FSC)
>>>         If failure had no penalty success would not be a prize
>>>                                                 -- T.  Pratchett
>>
>>
> I seeem to recall 0 coming up negative in some old IBM mainframes.
> That was an artifact of the way signed numbers were converted to
> binary.
>
> Tam
Not quite, but close. The ones-complement is to convert all zeroes to
one
and all ones to zero.
The twos-complement is the same as the ones-complement but then one is
Thus a negative zero is created by from binary 00000000 to become
11111111 which represents -1. By adding 1, we obtain (1)00000000
and the register, being unable to hold the 9th digit, is said to
overflow,
leaving 00000000.
This is a software matter that is independent of IBM.
When the numbers are fractional, as would be needed for sines
and cosines, etc, the difference between 0.999 and 1.0 is seldom
significant, but the difference between -1 and 0 is a catastrophe.

When I was test engineering for flight simulators, the DC9 sits
on the runway with the nose pitched down by 0.5 degrees. Upon
take off, it passes through zero and the pitch becomes positive.
Exacly a zero degrees, the image flipped upside down and displayed
the runway from the tail, going away, instead of the forward view,
then flipped back to normal. Failing to use the 2's complement
was the cause.
Androcles.

```
 0
Reply Androcles 12/20/2004 4:25:14 PM

```John Woodgate <jmw@jmwa.demon.contraspam.yuk> writes:

> I read in sci.electronics.design that Gactimus <gactimus@xrs.net> wrote
> (in <10sdnunotbnere2@corp.supernews.com>) about 'Is zero even or odd?',
> on Mon, 20 Dec 2004:
>>I know 0 is neither negative or positive but what about odd/even? I think
>>it's even.
>>
>>Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>>Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>
> There is other evidence. Even powers of negative numbers are positive,
> and (-x)^0 = 1, which is usually positive. (;-)

(-0)^2 = -0

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/20/2004 4:59:14 PM

```Gactimus wrote:
> I know 0 is neither negative or positive but what about odd/even? I think
> it's even.

It's a placeholder you twit.

```
 0
Reply Morituri 12/20/2004 5:21:20 PM

```I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
(in <x5d5x4nbx9.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
Mon, 20 Dec 2004:
>(-0)^2 = -0
>
>--
>David Kastrup, Kriemhildstr. 15, 44793 Bochum

Not even in Bochum. (;-)

Lim{x->0}[(-x^)2] = 0
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/20/2004 5:31:38 PM

```Androcles wrote:
> "Tam/WB2TT" <t-tammaru@c0mca\$t.net> wrote in message
>
>>"BB" <BB@BB.BB> wrote in message
>>news:10sdomrcqe6qt0e@corp.supernews.com...
>>
>>>Josef Moellers wrote:
>>>
>>>>Gactimus wrote:
>>>>
>>>>>I know 0 is neither negative or positive but what about odd/even?
>>>>>I think
>>>>>it's even.
>>>>>
>>>>>Odd numbers start at 1 and go every other number
>>>>>1,3,5,7;1,-1,-3,-5,-7
>>>>>Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>>>
>>>>As it can be divided by 2 without a remainder, it is obviously even.
>>>
>>>The divisor would have to be something smaller than 0 like -2.
>>>Therefore zero is both even and negative.
>>>
>>>
>>>>--
>>>>Josef M�llers (Pinguinpfleger bei FSC)
>>>>        If failure had no penalty success would not be a prize
>>>>                                                -- T.  Pratchett
>>>
>>>
>>I seeem to recall 0 coming up negative in some old IBM mainframes.
>>That was an artifact of the way signed numbers were converted to
>>binary.
>>
>>Tam
>
> Not quite, but close. The ones-complement is to convert all zeroes to
> one
> and all ones to zero.
> The twos-complement is the same as the ones-complement but then one is
> Thus a negative zero is created by from binary 00000000 to become
> 11111111 which represents -1. By adding 1, we obtain (1)00000000
> and the register, being unable to hold the 9th digit, is said to
> overflow,
> leaving 00000000.
> This is a software matter that is independent of IBM.

Before 1964, twos-complement was not at all universal. Both
ones-complement (-1 = 111110) and sign/absolute (-1 = 100001) were to be
seen. (Some machines weren't even binary.) Unique representation of zero
was one reason that twos-complement eventually won out.

--
John W. Kennedy
"You can, if you wish, class all science-fiction together; but it is
about as perceptive as classing the works of Ballantyne, Conrad and W.
W. Jacobs together as the 'sea-story' and then criticizing _that_."
-- C. S. Lewis.  "An Experiment in Criticism"
```
 0
Reply John 12/20/2004 6:08:13 PM

```"John W. Kennedy" <jwkenne@attglobal.net> wrote in message
news:1EExd.8182\$b52.2147@fe12.lga...
> Androcles wrote:
>> "Tam/WB2TT" <t-tammaru@c0mca\$t.net> wrote in message
>>
>>>"BB" <BB@BB.BB> wrote in message
>>>news:10sdomrcqe6qt0e@corp.supernews.com...
>>>
>>>>Josef Moellers wrote:
>>>>
>>>>>Gactimus wrote:
>>>>>
>>>>>>I know 0 is neither negative or positive but what about odd/even?
>>>>>>I think
>>>>>>it's even.
>>>>>>
>>>>>>Odd numbers start at 1 and go every other number
>>>>>>1,3,5,7;1,-1,-3,-5,-7
>>>>>>Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>>>>
>>>>>As it can be divided by 2 without a remainder, it is obviously
>>>>>even.
>>>>
>>>>The divisor would have to be something smaller than 0 like -2.
>>>>Therefore zero is both even and negative.
>>>>
>>>>
>>>>>--
>>>>>Josef M�llers (Pinguinpfleger bei FSC)
>>>>>        If failure had no penalty success would not be a prize
>>>>>                                                -- T.  Pratchett
>>>>
>>>>
>>>I seeem to recall 0 coming up negative in some old IBM mainframes.
>>>That was an artifact of the way signed numbers were converted to
>>>binary.
>>>
>>>Tam
>>
>> Not quite, but close. The ones-complement is to convert all zeroes to
>> one
>> and all ones to zero.
>> The twos-complement is the same as the ones-complement but then one
>> Thus a negative zero is created by from binary 00000000 to become
>> 11111111 which represents -1. By adding 1, we obtain (1)00000000
>> and the register, being unable to hold the 9th digit, is said to
>> overflow,
>> leaving 00000000.
>> This is a software matter that is independent of IBM.
>
> Before 1964, twos-complement was not at all universal. Both
> ones-complement (-1 = 111110) and sign/absolute (-1 = 100001) were to
> be seen. (Some machines weren't even binary.) Unique representation of
> zero was one reason that twos-complement eventually won out.

Egads... Aircraft flew on analogue machines then. Concorde was using DTL
for self-test only in 1977, I designed the test for the self test
computer using
state of the art EPROM.
Androcles.

>
> --
> John W. Kennedy
> "You can, if you wish, class all science-fiction together; but it is
> about as perceptive as classing the works of Ballantyne, Conrad and W.
> W. Jacobs together as the 'sea-story' and then criticizing _that_."
>   -- C. S. Lewis.  "An Experiment in Criticism"

```
 0
Reply Androcles 12/20/2004 6:37:27 PM

```John Woodgate <jmw@jmwa.demon.contraspam.yuk> writes:

> I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
> (in <x5d5x4nbx9.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
> Mon, 20 Dec 2004:
>>(-0)^2 = -0
>>
>
> Not even in Bochum. (;-)
>
> Lim{x->0}[(-x^)2] = 0

Either you mangled your parentheses, or this is a insidious way of
sneaking in a smilie.

If the former: in what respect does this negate my statement?  While
the limit need not necessarily be the same as the value itself (a
frequent mistake when talking about 0^0), we actually _do_ arrive at
the same result even in the limit here.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/20/2004 6:56:40 PM

```On Mon, 20 Dec 2004 15:50:04 GMT, "Androcles" <dummy@dummy.net> wrote:

>> Zero has no sign. Consider:
>>
>> If zero was positive, 1+0 > 1, but 1+0 = 0
>> If zero was negative, 1+0 < 1, but 1+0 = 0
>
>I thought 1+0 = 1, but I guess I can't do hard sums.
>Androcles.

---
Aaargghhh!!!

LOL!, Neither can I, obviously!

--
John Fields
```
 0
Reply John 12/20/2004 6:59:46 PM

```"John Fields" <jfields@austininstruments.com> wrote in message
news:i38es0hm84fs7esii5go3qgo7lodeh7n5e@4ax.com...
> On Mon, 20 Dec 2004 15:50:04 GMT, "Androcles" <dummy@dummy.net> wrote:
>
>
>>> Zero has no sign. Consider:
>>>
>>> If zero was positive, 1+0 > 1, but 1+0 = 0
>>> If zero was negative, 1+0 < 1, but 1+0 = 0
>>
>>I thought 1+0 = 1, but I guess I can't do hard sums.
>>Androcles.
>
> ---
> Aaargghhh!!!
>
> LOL!, Neither can I, obviously!
>
> --
> John Fields

Don't feel too bad. Neither could Einstein.
Androcles

```
 0
Reply Androcles 12/20/2004 7:11:01 PM

```On Mon, 20 Dec 2004 09:21:25 -0600, John Sefton <john@petcom.com>
wrote:

>It's not a prime, because a prime can
>only be divided by itself and 1.

---
That's not true.  A prime can be divided by anything, but an integer
greater than one is prime if its only positive divisors are itself and
one, but zero isn't prime because it's even.
---

>0 can't be divided by itself,

---
Sure it can. Anything (or nothing) divided by itself = 1
---

>but
>can be divided by everything else.
>An anti-prime?

---
No, an infinity.

--
John Fields
```
 0
Reply John 12/20/2004 7:19:34 PM

```In article <10sdnunotbnere2@corp.supernews.com>, Gactimus
<gactimus@xrs.net> wrote:

> I know 0 is neither negative or positive but what about odd/even? I think
> it's even.
>
> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
------
In all the math. classes I ever took, zero was regarded as an even
integer, neither positive nor negative, and not a prime number.

As to its sign, there is an ambiguity.  The signum function often gives
positive numbers a +1 value, negative numbers a -1 value, and zero a 0
value.  In machines using IEEE 754 floating point numbers there are
actually two kinds of zero defined, +0 and -0, and they have different
binary representations.  This can be seen in matlab as follows:

format hex
x = 0; y = -x;
[x,y]
ans = 0000000000000000   8000000000000000

To all intents and purposes, matlab treats these as the same number, as
in, for example,

x==y
ans = 1

However, the difference (aside from using format hex) can be detected with

sprintf('%+2.0f\n',x)
ans = +0
sprintf('%+2.0f\n',y)
ans = -0
--
(Remove "xyzzy" and ".invalid" to send me email.)
Roger Stafford
```
 0
Reply ellieandrogerxyzzy (4805) 12/20/2004 8:03:30 PM

```"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in
message
> In article <10sdnunotbnere2@corp.supernews.com>, Gactimus
> <gactimus@xrs.net> wrote:
>
>> I know 0 is neither negative or positive but what about odd/even? I think
>> it's even.
>>
>> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
> ------
>  In all the math. classes I ever took, zero was regarded as an even
> integer, neither positive nor negative, and not a prime number.
>
>  As to its sign, there is an ambiguity.  The signum function often gives
> positive numbers a +1 value, negative numbers a -1 value, and zero a 0
> value.  In machines using IEEE 754 floating point numbers there are
> actually two kinds of zero defined, +0 and -0, and they have different
> binary representations.  This can be seen in matlab as follows:
>
> format hex
> x = 0; y = -x;
> [x,y]
> ans = 0000000000000000   8000000000000000
>
> To all intents and purposes, matlab treats these as the same number, as
> in, for example,
>
> x==y
> ans = 1
>
> However, the difference (aside from using format hex) can be detected with
>
> sprintf('%+2.0f\n',x)
> ans = +0
> sprintf('%+2.0f\n',y)
> ans = -0
> --
> (Remove "xyzzy" and ".invalid" to send me email.)
> Roger Stafford

This from Mathworld (http://mathworld.wolfram.com/EvenNumber.html, Eric
Weisstein's phenomenal online math reference book):

An even number is an integer of the form , where k is an integer. The even
numbers are therefore ..., -4, -2, 0, 2, 4, 6, 8, 10, ... (Sloane's
A005843). Since the even numbers are integrally divisible by two, the
congruence  holds for even n.

Cheers,
Brett

begin 666 eimg3764.gif
M1TE&.#EA- `/`+,``````)F9F7=W=U555>[N[C,S,\S,S!\$1\$:JJJHB(B&9F
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begin 666 eimg3766.gif
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M9O___T1\$1-W=W2(B(KN[NR'Y! \$```L`+ ````!K`!\`0 3^<,E)J[TXZ\V[
MKTTC&>(%G&@:5 ] `4_6`,34&(N!+\U33X2'KZ);P"X&@\$ B."X(+LMN]/M@
M"(E\$-3- 6"6/Z22\&%H1@Z]ZS6Z[WW!!"5[>;AI+3&MW2%P\$@(&"8@L)41).
M?WE,#!-.#\$L,C8Z AT8Q7(L3@'2=GI^@H:*CI*6FGYP+`RL:!I.>B14,. 8'
MB[,6<@P.-0&O;\$TOF!<)FDTQ4'D%2S,[M2(.>4G#& VV% )^%<N,! IO!ZR^
M&@\%V*^/2TG.!PU0K-,8"=& OP74IQ\"K/G\$FOT``PH<2+"@P8,(\$RI46\$P!
M/PW[.AEP\$(L"`0\$,!F@K]*^4DP?!!S9T`55QA -,`P"40&/!6X\$``M!L!&:I
MY!AS3 `L0Z# 84P'.Q P\$%)@1P,&"6#:S#\$A995[%0) \;) 09I<@K(2"N8(
M'S9C."])@+0`XPL\$`51VW<#@VU<+\T8`,\$"539(2S3(4.[=V`5D%88T\$2%ME
M:=D\"(9ELZ!\$0H*>A(RDF/P03-%RD2G,^!&@@"T\`!0T"'#@Y8+.:*&6<8!6
D`8 !<VQ,#@ME(9%?! G@LEU!3D\$\O(,+'TZ\N/'CR/-%```[
`
end

```
 0
Reply shoelson.no.spam (1038) 12/20/2004 8:18:29 PM

```In article <10sdnunotbnere2@corp.supernews.com>,
Gactimus <gactimus@xrs.net> wrote:

> I know 0 is neither negative or positive but what about odd/even? I think
> it's even.
>
> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

The usual definition of an even integer (non-integers are neither even
nor odd) is that N is an even integer iff n = 2*m for some integer m.

Is 0 = 2*m for some integer m?
```
 0
Reply Virgil 12/20/2004 8:38:28 PM

```John Fields <jfields@austininstruments.com> writes:

> On Mon, 20 Dec 2004 09:21:25 -0600, John Sefton <john@petcom.com>
> wrote:
>
>
>>It's not a prime, because a prime can
>>only be divided by itself and 1.
>
> ---
> That's not true.  A prime can be divided by anything, but an integer
> greater than one is prime if its only positive divisors are itself and
> one, but zero isn't prime because it's even.
> ---
>
>>0 can't be divided by itself,
>
> ---
> Sure it can. Anything (or nothing) divided by itself = 1

Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/20/2004 8:43:14 PM

```Nicholas O. Lindan wrote:
> "John Sefton" <john@petcom.com> wrote
>
>
>>0 can't be divided by itself,
>
>
> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
> It works if the only three numbers in the universe are
> 0, 1, and infinity -- A number system that seems very
> suited to usenet.
>

Zero is even. You cannot divide by zero. Limits are not division.
Infinity is not a number. Computers bugger up the system.

--- Shawn
```
 0
Reply Shawn 12/20/2004 8:43:59 PM

```"David Kastrup" <dak@gnu.org> wrote in message

> > 0/0 = 1

> Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?

Not so fast, if 0/0 = 1 then it follows:

0 + 0 = 2 * 0

1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/20/2004 8:54:02 PM

```"Virgil" <ITSnetNOTcom#virgil@COMCAST.com> wrote in message
news:ITSnetNOTcom%23virgil-2A1122.13382820122004@[63.218.45.211]...
> In article <10sdnunotbnere2@corp.supernews.com>,
>  Gactimus <gactimus@xrs.net> wrote:
>
> > I know 0 is neither negative or positive but what about odd/even? I
think
> > it's even.
> >
> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>
> The usual definition of an even integer (non-integers are neither even
> nor odd) is that N is an even integer iff n = 2*m for some integer m.
>
> Is 0 = 2*m for some integer m?

Yes.  0 is an integer, and 0 = (2) (0), so therefore 0 is an even integer.
(Just to clarify, integers are defined as the set {...-3, -2, -1, 0, 1, 2,
3, ...} )

```
 0
Reply Richards 12/20/2004 8:56:31 PM

```I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
(in <x5oegolrx3.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
Mon, 20 Dec 2004:
>John Woodgate <jmw@jmwa.demon.contraspam.yuk> writes:
>
>> I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
>> (in <x5d5x4nbx9.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
>> Mon, 20 Dec 2004:
>>>(-0)^2 = -0
>>>
>>
>> Not even in Bochum. (;-)
>>
>> Lim{x->0}[(-x^)2] = 0
>
>Either you mangled your parentheses, or this is a insidious way of
>sneaking in a smilie.

Nothing is mangled if you view plain text. What HTML might make of it, I
don't know.
>
>If the former: in what respect does this negate my statement?  While the
>limit need not necessarily be the same as the value itself (a frequent
>mistake when talking about 0^0), we actually _do_ arrive at the same
>result even in the limit here.

Your equation claims that a certain *real* number squared is a negative
number. '-0' passes the test of a real number in that it is the root of
(innumerable) algebraic equations with integer coefficients, such as
4576238x^2 = 0, solution x = +/-0. Its square must be positive.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/20/2004 9:01:20 PM

```I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
(in <x5mzw8k8f1.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
Mon, 20 Dec 2004:

>Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?

0/0 can take ANY value.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/20/2004 9:02:32 PM

```I read in sci.electronics.design that Virgil <ITSnetNOTcom#virgil@COMCAS
T.com> wrote (in <ITSnetNOTcom#virgil-2A1122.13382820122004@[63.218.45.2
11]>) about 'Is zero even or odd?', on Mon, 20 Dec 2004:
>In article <10sdnunotbnere2@corp.supernews.com>,
> Gactimus <gactimus@xrs.net> wrote:
>
>> I know 0 is neither negative or positive but what about odd/even? I think
>> it's even.
>>
>> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>
>The usual definition of an even integer (non-integers are neither even
>nor odd) is that N is an even integer iff n = 2*m for some integer m.
>
>Is 0 = 2*m for some integer m?

Yes. m = 0. 0 is clearly not a non-integer.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/20/2004 9:04:15 PM

```Yes!
```
 0
Reply Virgil 12/20/2004 9:09:12 PM

```John Fields wrote:

> That's not true.  A prime can be divided by anything, but an integer
> greater than one is prime if its only positive divisors are itself and
> one, but zero isn't prime because it's even.

And two isn't prime because it's even?
```
 0
Reply George 12/20/2004 9:54:18 PM

```"John Woodgate" <jmw@jmwa.demon.contraspam.yuk> wrote in message
news:QM1RleEHRvxBFwlq@jmwa.demon.co.uk...
> I read in sci.electronics.design that Nicholas O. Lindan
<see@sig.com>
> 'Is zero even or odd?', on Mon, 20 Dec 2004:
>
> >"John Sefton" <john@petcom.com> wrote
> >
> >> 0 can't be divided by itself,
> >
> >Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
> One possible solution, given the enormous lack of rigour in
'infinity'.

There is no lack of rigour in the definition of infinity.  Read anbout
the work of Cantor, Dedekind and others.

[snip]

Franz

```
 0
Reply Franz 12/20/2004 10:19:46 PM

```"David Kastrup" <dak@gnu.org> wrote in message
news:x5d5x4nbx9.fsf@lola.goethe.zz...

[snip]

> (-0)^2 = -0

Not on my Casio calculator.

Franz

```
 0
Reply Franz 12/20/2004 10:19:47 PM

```John Woodgate <jmw@jmwa.demon.contraspam.yuk> writes:

> I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
> (in <x5mzw8k8f1.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
> Mon, 20 Dec 2004:
>
>>Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?
>
> 0/0 can take ANY value.

Well, and in the above it takes on 1, so that would be quite legal,
right?

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/20/2004 10:34:25 PM

```Shawn Corey, lun20041220@21:43:59(CET):
>
> Zero is even. You cannot divide by zero. Limits are not division.
> Infinity is not a number. Computers bugger up the system.

That could be said louder, but not clearer :).

--
David Serrano
```
 0
Reply Hue 12/20/2004 10:35:54 PM

```"Franz Heymann" <notfranz.heymann@btopenworld.com> writes:

> "David Kastrup" <dak@gnu.org> wrote in message
> news:x5d5x4nbx9.fsf@lola.goethe.zz...
>
> [snip]
>
>> (-0)^2 = -0
>
> Not on my Casio calculator.

What else is it there?

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/20/2004 10:35:55 PM

```BB wrote:
> Josef Moellers wrote:
>>
>> Gactimus wrote:
>>> I know 0 is neither negative or positive but what about odd/even? I
>>> think it's even.
>>>
>>> Odd numbers start at 1 and go every other number
>>> 1,3,5,7;1,-1,-3,-5,-7 Even starts at 2 and go every other number
>>> 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> As it can be divided by 2 without a remainder, it is obviously even.
>
> The divisor would have to be something smaller than 0 like -2.
> Therefore zero is both even and negative.

I'm sorry, sir, but 0 is universally defined in math to be neither - nor
+, it's jsut 0. Many graphing and soem scientific calculators have a
sign function. On any calc I've tried this on, it gives -1 for any
negative number, it gives a 1 for ant positive value, and 0 (zero) for,
well, 0 (zero.) As is defined in basic math.

```
 0
Reply Alfred 12/20/2004 11:18:47 PM

```Nicholas O. Lindan wrote:
> "John Sefton" <john@petcom.com> wrote
>
>> 0 can't be divided by itself,
>
> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
> It works if the only three numbers in the universe are
> 0, 1, and infinity -- A number system that seems very
> suited to usenet.

Except for the fact that: 0 / 0 = undefined

Or actually more correct: n / 0 = undefined

```
 0
Reply Alfred 12/20/2004 11:21:14 PM

```John Woodgate wrote:
> I read in sci.electronics.design that David Kastrup <dak@gnu.org>
> wrote (in <x5mzw8k8f1.fsf@lola.goethe.zz>) about 'Is zero even or
> odd?', on Mon, 20 Dec 2004:
>
>> Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?
>
> 0/0 can take ANY value.

n / 0 = undefined

```
 0
Reply Alfred 12/20/2004 11:25:26 PM

```Nicholas O. Lindan wrote:
>
> 1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2
>

a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b  = b
but a = b
a+a = a
2a = a
2 = 1

What could be clearer?

--- Shawn
```
 0
Reply Shawn 12/21/2004 12:21:43 AM

```On Mon, 20 Dec 2004 19:21:43 -0500, Shawn Corey
<shawn.corey@sympatico.ca> wrote:

>Nicholas O. Lindan wrote:
>>
>> 1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2
>>
>
>          a = b
>        a^2 = ab
>  a^2 - b^2 = ab - b^2
>(a+b)(a-b) = b(a-b)
>       a+b  = b
>but a = b
>        a+a = a
>         2a = a
>          2 = 1
>
>What could be clearer?
>
>    --- Shawn

I remember that one from when I was in high school ;-)

...Jim Thompson
--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |

I love to cook with wine.      Sometimes I even put it in the food.
```
 0
Reply Jim 12/21/2004 12:32:31 AM

```"Shawn Corey" <shawn.corey@sympatico.ca> wrote
>           a = b
>         a^2 = ab
>   a^2 - b^2 = ab - b^2
> (a+b)(a-b) = b(a-b)
>        a+b  = b
> but a = b
>         a+a = a
>          2a = a
>           2 = 1

Now if we can just get the IRS to agree.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com

```
 0
Reply Nicholas 12/21/2004 1:05:34 AM

```
Alfred Z. Newmane wrote:
> Nicholas O. Lindan wrote:
>
>>"John Sefton" <john@petcom.com> wrote
>>
>>
>>>0 can't be divided by itself,
>>
>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>
>>It works if the only three numbers in the universe are
>>0, 1, and infinity -- A number system that seems very
>>suited to usenet.
>
>
> Except for the fact that: 0 / 0 = undefined
>
> Or actually more correct: n / 0 = undefined
>
>

0/0={ SET OF ALL INTEGERS }

n/0= NULL SET  for n<>0

It is very well-defined.

```
 0
Reply Fred 12/21/2004 1:08:55 AM

```David Kastrup wrote:
> John Woodgate <jmw@jmwa.demon.contraspam.yuk> writes:
>
>> I read in sci.electronics.design that Gactimus <gactimus@xrs.net>
>> wrote (in <10sdnunotbnere2@corp.supernews.com>) about 'Is zero even
>> or odd?', on Mon, 20 Dec 2004:
>>> I know 0 is neither negative or positive but what about odd/even? I
>>> think it's even.
>>>
>>> Odd numbers start at 1 and go every other number
>>> 1,3,5,7;1,-1,-3,-5,-7 Even starts at 2 and go every other number
>>> 2,4,6,8;2,0,-2,-4,-6,-8
>>
>> There is other evidence. Even powers of negative numbers are
>> positive, and (-x)^0 = 1, which is usually positive. (;-)
>
> (-0)^2 = -0

No, it's just 9. You dont have +0 or -0, it's just 0 (zero.) Writing it
as +0 or -0 still is jsut 0 sicne 0 has no sign. You have +, -, and 0.
Or for what you get from any proper sign function, either 1, -1, or 0.

```
 0
Reply Alfred 12/21/2004 1:40:24 AM

```Franz Heymann wrote:
> "David Kastrup" <dak@gnu.org> wrote in message
> news:x5d5x4nbx9.fsf@lola.goethe.zz...
>
> [snip]
>
>> (-0)^2 = -0
>
> Not on my Casio calculator.

Thats becuase, when translated to reality, that statement becomes (0)^2
= 0, because 0 has no sign. I really wish people would stop trying to
spread the false hood that0 actually has a sign.

```
 0
Reply Alfred 12/21/2004 1:44:11 AM

```On Mon, 20 Dec 2004 14:21:11 -0000, Gactimus <gactimus@xrs.net> wrote:

>I know 0 is neither negative or positive but what about odd/even? I think
>it's even.

0 has no flat edges, so it can't be even.
```
 0
Reply Jim 12/21/2004 2:24:05 AM

```In article <32pd7rF3q16ikU1@individual.net>,
Alfred Z. Newmane <a.newmane.remove@eastcoastcz.com> wrote:

>You dont have +0 or -0, it's just 0 (zero.)

No, you *do* have +0 and -0, and they are both equal to 0.

-- Richard
```
 0
Reply richard 12/21/2004 2:36:55 AM

```On Mon, 20 Dec 2004 19:21:43 -0500, Shawn Corey wrote:

> Nicholas O. Lindan wrote:
>>
>> 1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2
>>
>>
>           a = b
>         a^2 = ab
>   a^2 - b^2 = ab - b^2
> (a+b)(a-b) = b(a-b)
>        a+b  = b
> but a = b
>         a+a = a
>          2a = a
>           2 = 1
>
> What could be clearer?

I used to know a proof along these lines:

-----

x = +1
A = [integral] f(x) dx
x = -1

By examining a graph, it is obvious that A > 0.

Let y = 1/x, therefore x = 1/y, and substitute this into the equation:

x = +1
A = [integral] f(1/y) f'(y) dy
x = -1

The right-hand side is clearly equivalent to -A

A = -A

A = 0

-----

Unfortunately, I don't remember which f(x) causes this to work.  I'm
pretty sure it was a fairly simple trigonometric operation.

```
 0
Reply Ed 12/21/2004 2:44:00 AM

```Jim Ward wrote:
> On Mon, 20 Dec 2004 14:21:11 -0000, Gactimus <gactimus@xrs.net> wrote:
>
>> I know 0 is neither negative or positive but what about odd/even? I
>> think it's even.
>
> 0 has no flat edges, so it can't be even.

It does on my digital clock (as does my digital watch) :-P

```
 0
Reply Alfred 12/21/2004 2:47:18 AM

```Richard Tobin wrote:
> In article <32pd7rF3q16ikU1@individual.net>,
> Alfred Z. Newmane <a.newmane.remove@eastcoastcz.com> wrote:
>
>> You dont have +0 or -0, it's just 0 (zero.)
>
> No, you *do* have +0 and -0, and they are both equal to 0.

Well I basically said that in the part you didn't quote :-)

```
 0
Reply Alfred 12/21/2004 2:48:23 AM

```John Woodgate wrote:
>>>Lim{x->0}[(-x^)2] = 0
>>Either you mangled your parentheses, or this is a insidious way of
>>sneaking in a smilie.
> Nothing is mangled if you view plain text.

Perhaps you could explain what (-x^)2 means then?
```
 0
Reply Clifford 12/21/2004 3:43:17 AM

```I remember this as a homework problem in 9th grade algebra class many years
ago.  More recently, my son encounted the same question in 7th grade algebra
class as an extra credit homework question. He did well but failed to realized
that one cannot just assume that zero must be even or odd but not both. Most
other students make the same mistake.  The basic proof provided by many of us
in my algebra class is listed below:

--------

Homework question:
Is zero and even number or an odd number?

Math definitions:
Even numbers are numbers that can be written in the form 2n,
where n is an integer.
Odd numbers are numbers that can be written in the form 2n + 1,
where n is an integer.

First question and answer:
Is zero an even number?
That is: Is there an integer n, such that 0 = 2n ?
Yes.  0=2n  =>  0/2=n  =>  0=n (an obvious integer)
Therefore, 0 is an even number because if can satisfy the definition.

Second question and answer:
Is zero an odd number?
That is: Is there an integer n, such that 0 = 2n +1 ?
No.   0=2n+1  =>  -1=2n   =>  -1/2=n  which shows that n can not
be an integer in this case.
Therefore, 0 is not an odd number because it fails to satisfy the
definition.

--------

Any other math fact about even and odd numbers aren't needed to answer
the simple question "Is zero even, odd or both?"   Of course, other facts about
even & odd numbers can be used to answer the question if those facts have
been rigorously proven. For example:  A number is even if and only if it is the
sum of 2 even numbers.

Note that we cannot automatically assume that the set of even numbers and the
set of odd numbers are mutually exclusive just from the definitions above.  Of
course, the proof of this fact is rather trivial:
x = 2n   plus   x=2m+1    =>
2n=2m+1              =>
2n/2 = 2m/2 +1/2     =>
n=m+1/2, which is impossible since n & m must both be integers

Based just upon the definitions, we also cannot make the assumption that every
integer must satisfy at least one of the definitions above and must therefore
be even or odd.

I point these out because the even/odd situation is an early introduction to
number theory and primative proofs for young students.  And most students fall
into the trap of making assumptions which are not supported by the definitions
alone:
1)  All even or odd numbers must be integers
2)  All integers must be even or odd numbers
3)  A number cannot be both even and odd

All three statements above are true but must be substantiated via proofs.

The debate over whether zero is positive or negative is also solved rather
quickly by reverting to the math definitions:
Positive numbers are numbers that are greater than zero.
Negative numbers are numbers that are less than zero.

```
 0
Reply Gideon 12/21/2004 5:15:26 AM

```In article <10sdnunotbnere2@corp.supernews.com>, Gactimus wrote:
>I know 0 is neither negative or positive but what about odd/even? I think
>it's even.
>
>Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

Zero is definitely even.  Dividing zero by 2 leaves no "remainder" or
"fraction".

However, as a bit of a digression, there are "odd functions" and "even
functions" - odd ones must have output zero when input is zero.  Even
functions are permitted to have output zero or nonzero when input is
zero.
Functions can be odd, even or neither.  With an even function, F(x) =
F(-x).  With an odd function, F(-x) = -F(x).

- Don Klipstein (don@misty.com)
```
 0
Reply don 12/21/2004 6:03:04 AM

```John Fields wrote:
> On Mon, 20 Dec 2004 09:21:25 -0600, John Sefton <john@petcom.com>
> wrote:
>
>
>> It's not a prime, because a prime can
>> only be divided by itself and 1.
>
> ---
> That's not true.  A prime can be divided by anything, but an integer
> greater than one is prime if its only positive divisors are itself and
> one, but zero isn't prime because it's even.
> ---
>
>> 0 can't be divided by itself,
>
> ---
> Sure it can.

No it cant.

> Anything (or nothing) divided by itself = 1

O is specifically excluded from this result as dividing by zero causes

Division by zero is *defined* to be undefined. And my usual, "this is
not debatable" applies to this one. Read it up in any text book.

The limit:

L = f(x)/g(x) x->xo, where f(xo)=g(xo)=0

May or may not exist. If it dose, the limit may be any specific value
depending on the way the limit is approached.

In many case the *limit* represents physical reality. The notation 0/0
is a limit, and as such, is meaningless in mathematics.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/21/2004 7:08:09 AM

```Fred Bloggs wrote:
> Alfred Z. Newmane wrote:
>> Nicholas O. Lindan wrote:
>>
>>> "John Sefton" <john@petcom.com> wrote
>>>
>>>
>>>> 0 can't be divided by itself,
>>>
>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>
>>> It works if the only three numbers in the universe are
>>> 0, 1, and infinity -- A number system that seems very
>>> suited to usenet.
>>
>>
>> Except for the fact that: 0 / 0 = undefined
>>
>> Or actually more correct: n / 0 = undefined
>>
>>
>
> 0/0={ SET OF ALL INTEGERS }

No.

>
> n/0= NULL SET  for n<>0
>
> It is very well-defined.

No it isnt.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/21/2004 7:08:11 AM

```you can say that again! Hilarious!

"Nicholas O. Lindan" wrote:

> "John Sefton" <john@petcom.com> wrote
>
> > 0 can't be divided by itself,
>
> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
> It works if the only three numbers in the universe are
> 0, 1, and infinity -- A number system that seems very
> suited to usenet.
>
> --
> Nicholas O. Lindan, Cleveland, Ohio
> Consulting Engineer:  Electronics; Informatics; Photonics.
> Remove spaces etc. to reply: n o lindan at net com dot com
> psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

```
 0
Reply Bondo 12/21/2004 7:23:02 AM

```Nice statement. However, this 'proves' once again to me that I
was never any good at math because I'm nogood at thinking, just
too lazy! What a shame.
Bondo

Gideon wrote:

> I remember this as a homework problem in 9th grade algebra class many years
> ago.  More recently, my son encounted the same question in 7th grade algebra
> class as an extra credit homework question. He did well but failed to realized
> that one cannot just assume that zero must be even or odd but not both. Most
> other students make the same mistake.  The basic proof provided by many of us
> in my algebra class is listed below:
>
> --------
>
> Homework question:
>      Is zero and even number or an odd number?
>
> Math definitions:
>      Even numbers are numbers that can be written in the form 2n,
>      where n is an integer.
>      Odd numbers are numbers that can be written in the form 2n + 1,
>      where n is an integer.
>
> First question and answer:
>      Is zero an even number?
>      That is: Is there an integer n, such that 0 = 2n ?
>      Yes.  0=2n  =>  0/2=n  =>  0=n (an obvious integer)
>      Therefore, 0 is an even number because if can satisfy the definition.
>
> Second question and answer:
>      Is zero an odd number?
>      That is: Is there an integer n, such that 0 = 2n +1 ?
>      No.   0=2n+1  =>  -1=2n   =>  -1/2=n  which shows that n can not
>      be an integer in this case.
>      Therefore, 0 is not an odd number because it fails to satisfy the
>      definition.
>
> --------
>
> Any other math fact about even and odd numbers aren't needed to answer
> the simple question "Is zero even, odd or both?"   Of course, other facts about
> even & odd numbers can be used to answer the question if those facts have
> been rigorously proven. For example:  A number is even if and only if it is the
> sum of 2 even numbers.
>
> Note that we cannot automatically assume that the set of even numbers and the
> set of odd numbers are mutually exclusive just from the definitions above.  Of
> course, the proof of this fact is rather trivial:
>     x = 2n   plus   x=2m+1    =>
>     2n=2m+1              =>
>     2n/2 = 2m/2 +1/2     =>
>     n=m+1/2, which is impossible since n & m must both be integers
>
> Based just upon the definitions, we also cannot make the assumption that every
> integer must satisfy at least one of the definitions above and must therefore
> be even or odd.
>
> I point these out because the even/odd situation is an early introduction to
> number theory and primative proofs for young students.  And most students fall
> into the trap of making assumptions which are not supported by the definitions
> alone:
>   1)  All even or odd numbers must be integers
>   2)  All integers must be even or odd numbers
>   3)  A number cannot be both even and odd
>
> All three statements above are true but must be substantiated via proofs.
>
> The debate over whether zero is positive or negative is also solved rather
> quickly by reverting to the math definitions:
>     Positive numbers are numbers that are greater than zero.
>     Negative numbers are numbers that are less than zero.

```
 0
Reply Bondo 12/21/2004 7:32:31 AM

```In sci.math,
comp.soft-sys.matlab,
sci.physics,
rec.puzzles,
sci.astro,
sci.electronics.design and
comp.lang.perl.misc, on Mon, 20 Dec 2004 21:02:32 +0000, John Woodgate
<jmw@jmwa.demon.contraspam.yuk> wrote:

>I read in sci.electronics.design that David Kastrup <dak@gnu.org> wrote
>(in <x5mzw8k8f1.fsf@lola.goethe.zz>) about 'Is zero even or odd?', on
>Mon, 20 Dec 2004:
>
>>Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?
>
>0/0 can take ANY value.

Furthermore, 0/0 can GIVE any value. What a versatile expression!

-----
```
 0
Reply Ben 12/21/2004 7:41:52 AM

```Nicholas O. Lindan wrote:
> "John Sefton" <john@petcom.com> wrote
>=20
>=20
>>0 can't be divided by itself,
>=20
>=20
> Sure it can: 0 / 0 =3D 0 * (1 / 0) =3D 0 * infinity =3D 1
>=20
> It works if the only three numbers in the universe are
> 0, 1, and infinity -- A number system that seems very
> suited to usenet.
>=20

Not only usenet: someone once postulated that the only three "values" to =

be used in providing computer resources should be 0, 1 and infinity=20
(which he meant to mean "unlimited" (for all practical purposes) (*)).

(*) My math teacher always said "A sphere's surface is unlimited but not =

infinite", just to highlight the difference between the two.
--=20
Josef M=F6llers (Pinguinpfleger bei FSC)
If failure had no penalty success would not be a prize
-- T.  Pratchett

```
 0
Reply Josef 12/21/2004 7:45:16 AM

```I read in sci.electronics.design that Clifford Heath <no@spam.please>
wrote (in <32pkemF3p3b5bU1@individual.net>) about 'Is zero even or
odd?', on Tue, 21 Dec 2004:
>John Woodgate wrote:
>>>>Lim{x->0}[(-x^)2] = 0
>>>Either you mangled your parentheses, or this is a insidious way of
>>>sneaking in a smilie.
>> Nothing is mangled if you view plain text.
>
>Perhaps you could explain what (-x^)2 means then?

How did you manage to move the ^? (;-)
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/21/2004 9:00:52 AM

```In article <kSDxd.34179\$jf5.6646@fe1.texas.rr.com>, "Morituri-|-Max" <newage@sendarico.net> writes:
>Gactimus wrote:
>> I know 0 is neither negative or positive but what about odd/even? I think
>> it's even.
>
>It's a placeholder you twit.
>
It is a valid number.  And it is even.

Mati Meron                      | "When you argue with a fool,
meron@cars.uchicago.edu         |  chances are he is doing just the same"
```
 0
Reply mmeron 12/21/2004 9:05:16 AM

```In article <32p53dF3paevvU1@individual.net>, "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> writes:
>Nicholas O. Lindan wrote:
>> "John Sefton" <john@petcom.com> wrote
>>
>>> 0 can't be divided by itself,
>>
>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>
>> It works if the only three numbers in the universe are
>> 0, 1, and infinity -- A number system that seems very
>> suited to usenet.
>
>Except for the fact that: 0 / 0 = undefined
>
>Or actually more correct: n / 0 = undefined
>
The two are not the same.

The definition of the ratio a/b is

a/b = r iff b*r = a

for the case of n/0 there is no r such that r*0 = n (follows from the
definition of zero.  Therefore n/0 (for non zero n) *does not exist*.

On the other hand, for 0/0, every r qualifies since for every r, r*0 =
0 (the definition of zero, again).  Therefore, 0/0 is truly undefined,
in the sense that it is impossible to *uniquely* assign a value to the
ratio r.

Mati Meron                      | "When you argue with a fool,
meron@cars.uchicago.edu         |  chances are he is doing just the same"
```
 0
Reply mmeron 12/21/2004 9:19:21 AM

```Fred Bloggs <nospam@nospam.com> writes:

> Alfred Z. Newmane wrote:
>> Nicholas O. Lindan wrote:
>>
>>>"John Sefton" <john@petcom.com> wrote
>>>
>>>
>>>>0 can't be divided by itself,
>>>
>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>
>>>It works if the only three numbers in the universe are
>>>0, 1, and infinity -- A number system that seems very
>>>suited to usenet.
>> Except for the fact that: 0 / 0 = undefined
>> Or actually more correct: n / 0 = undefined
>>
>
> 0/0={ SET OF ALL INTEGERS }
>
> n/0= NULL SET  for n<>0
>
> It is very well-defined.

So { SET OF ALL INTEGERS } = 0/0 = (0+0)/0 = (2*0)/0 = 2*(0/0)
= 2* {SET OF ALL INTEGERS } = {SET OF ALL EVEN INTEGERS}?

Odd.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/21/2004 10:30:37 AM

```"Kevin Aylward" <salesEXTRACT@anasoft.co.uk> writes:

> The limit:
>
> L = f(x)/g(x) x->xo, where f(xo)=g(xo)=0
>
> May or may not exist. If it dose, the limit may be any specific value
> depending on the way the limit is approached.
>
> In many case the *limit* represents physical reality. The notation
> 0/0 is a limit, and as such, is meaningless in mathematics.

Hogwash.  The notation 0/0 is most certainly not a limit, like 4/2 is
not a limit.  And how could you define a limit if there were no

0/0 is clearly, if anything, a constant expression.  And it turns out
that its value is undefined.  And limits have nothing to do with that.

There are "limits of the form 0/0", but this is a shorthand for
something completely different, and such limits in general _have_ a
value (depending on just what is taken to the limit here).

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/21/2004 10:36:05 AM

```
Kevin Aylward wrote:
> Fred Bloggs wrote:
>
>>Alfred Z. Newmane wrote:
>>
>>>Nicholas O. Lindan wrote:
>>>
>>>
>>>>"John Sefton" <john@petcom.com> wrote
>>>>
>>>>
>>>>
>>>>>0 can't be divided by itself,
>>>>
>>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>
>>>>It works if the only three numbers in the universe are
>>>>0, 1, and infinity -- A number system that seems very
>>>>suited to usenet.
>>>
>>>
>>>Except for the fact that: 0 / 0 = undefined
>>>
>>>Or actually more correct: n / 0 = undefined
>>>
>>>
>>
>>0/0={ SET OF ALL INTEGERS }
>
>
> No.
>
>
>>n/0= NULL SET  for n<>0
>>
>>It is very well-defined.
>
>
> No it isnt.
>
> Kevin Aylward

You apparently have stumbled on something else you know damn little
about. In case you need help with this , you might note that "/" is NOT
an operator on the integers, it is the "inverse" of a multiplication
operator. Inverse is a well-defined concept but not necessarily a
function, it is a set theoretic mapping. E.G. m/n={ q: m=q*n} by
definition, so that m/n which is actually a set which can be empty, a
singleton, or infinite. In the case of m/n, it is then m/n = F^-1(m)
where F(x)= n*x. Your reasoning would lead one to believe /: I x I -> I
is a function, which it isn't.

```
 0
Reply Fred 12/21/2004 10:37:35 AM

```"Gactimus" <gactimus@xrs.net> wrote in message
news:10sdnunotbnere2@corp.supernews.com...
:I know 0 is neither negative or positive but what about odd/even? I think
: it's even.
:
: Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
: Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

I think it's odd that you even need to ask...

--
Wyzelli
more into words than numbers...

```
 0
Reply Peter 12/21/2004 10:40:11 AM

```
David Kastrup wrote:
> Fred Bloggs <nospam@nospam.com> writes:
>
>
>>Alfred Z. Newmane wrote:
>>
>>>Nicholas O. Lindan wrote:
>>>
>>>
>>>>"John Sefton" <john@petcom.com> wrote
>>>>
>>>>
>>>>
>>>>>0 can't be divided by itself,
>>>>
>>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>
>>>>It works if the only three numbers in the universe are
>>>>0, 1, and infinity -- A number system that seems very
>>>>suited to usenet.
>>>
>>>Except for the fact that: 0 / 0 = undefined
>>>Or actually more correct: n / 0 = undefined
>>>
>>
>>0/0={ SET OF ALL INTEGERS }
>>
>>n/0= NULL SET  for n<>0
>>
>>It is very well-defined.
>
>
> So { SET OF ALL INTEGERS } = 0/0 = (0+0)/0 = (2*0)/0 = 2*(0/0)
>   = 2* {SET OF ALL INTEGERS } = {SET OF ALL EVEN INTEGERS}?
>
> Odd.
>

Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?

```
 0
Reply Fred 12/21/2004 10:40:32 AM

```David Kastrup wrote:
> "Kevin Aylward" <salesEXTRACT@anasoft.co.uk> writes:
>
>> The limit:
>>
>> L = f(x)/g(x) x->xo, where f(xo)=g(xo)=0
>>
>> May or may not exist. If it dose, the limit may be any specific value
>> depending on the way the limit is approached.

I should clarify this. This is referring to the notion that different
f(x) and g(x) will lead to different limits. Usually for the limit to
have meaning, it must be the same independent of the way a specific f(x)
and g(x) approaches the limit.

>>
>> In many case the *limit* represents physical reality. The notation
>> 0/0 is a limit, and as such, is meaningless in mathematics.
>
> Hogwash.  The notation 0/0 is most certainly not a limit, like 4/2 is

This was a typo, for which I apologise. It should have been abundantly
clear from the context that I was saying "is not a limit". Unfortunately
when I spell checked I inadvertently deleted a word.

The above wouldn't make logical sense at all otherwise, as I already
defined "L" a limit, and distinguished it from 0/0. How can a limit be
physically meaningfull, yet meaningless?

> not a limit.  And how could you define a limit if there were no
>
> 0/0 is clearly, if anything, a constant expression.  And it turns out
> that its value is undefined.

Which is what I said i.e. "0/0 is meaningless"

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/21/2004 11:03:41 AM

```Fred Bloggs wrote:
> Kevin Aylward wrote:
>> Fred Bloggs wrote:
>>
>>> Alfred Z. Newmane wrote:
>>>
>>>> Nicholas O. Lindan wrote:
>>>>
>>>>
>>>>> "John Sefton" <john@petcom.com> wrote
>>>>>
>>>>>
>>>>>
>>>>>> 0 can't be divided by itself,
>>>>>
>>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>
>>>>> It works if the only three numbers in the universe are
>>>>> 0, 1, and infinity -- A number system that seems very
>>>>> suited to usenet.
>>>>
>>>>
>>>> Except for the fact that: 0 / 0 = undefined
>>>>
>>>> Or actually more correct: n / 0 = undefined
>>>>
>>>>
>>>
>>> 0/0={ SET OF ALL INTEGERS }
>>
>>
>> No.
>>
>>
>>> n/0= NULL SET  for n<>0
>>>
>>> It is very well-defined.
>>
>>
>> No it isnt.
>>
>> Kevin Aylward
>
> You apparently have stumbled on something else you know damn little

There is a lot I don't know, but this isn't an example of such.

>In case you need help with this , you might note that "/" is
> NOT an operator on the integers,

No it isn't, it is an operator on all numbers, integer or otherwise.

>it is the "inverse" of a
> multiplication operator.

Sure, you can have *another* meaning to the / operator in a different
context, but this aint that context. This discussion is about a/b as
usually understood in arithmetic.

>Inverse is a well-defined concept but not
> necessarily a function, it is a set theoretic mapping. E.G. m/n={ q:
> m=q*n} by definition, so that m/n which is actually a set which can
> be empty, a singleton, or infinite.

My, my, aint you a clever dude...

>In the case of m/n, it is then
> m/n = F^-1(m) where F(x)= n*x. Your reasoning would lead one to
> believe /: I x I -> I is a function, which it isn't.

Nope. I am using a well understood definition of division as applicable
to this argument.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/21/2004 11:04:59 AM

```
Kevin Aylward wrote:
> Fred Bloggs wrote:
>
>>Kevin Aylward wrote:
>>
>>>Fred Bloggs wrote:
>>>
>>>
>>>>Alfred Z. Newmane wrote:
>>>>
>>>>
>>>>>Nicholas O. Lindan wrote:
>>>>>
>>>>>
>>>>>
>>>>>>"John Sefton" <john@petcom.com> wrote
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>0 can't be divided by itself,
>>>>>>
>>>>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>>
>>>>>>It works if the only three numbers in the universe are
>>>>>>0, 1, and infinity -- A number system that seems very
>>>>>>suited to usenet.
>>>>>
>>>>>
>>>>>Except for the fact that: 0 / 0 = undefined
>>>>>
>>>>>Or actually more correct: n / 0 = undefined
>>>>>
>>>>>
>>>>
>>>>0/0={ SET OF ALL INTEGERS }
>>>
>>>
>>>No.
>>>
>>>
>>>
>>>>n/0= NULL SET  for n<>0
>>>>
>>>>It is very well-defined.
>>>
>>>
>>>No it isnt.
>>>
>>>Kevin Aylward
>>
>>You apparently have stumbled on something else you know damn little
>
>
> There is a lot I don't know, but this isn't an example of such.
>
>
>>In case you need help with this , you might note that "/" is
>>NOT an operator on the integers,
>
>
> No it isn't, it is an operator on all numbers, integer or otherwise.

We were talking about integers, and therefore 0/0={all integers}. You
want to talk about reals then 0/0={ all reals }. Are you saying that 0*x
<> 0? If not then my answer is correct.

>
>
>>it is the "inverse" of a
>>multiplication operator.
>
>
> Sure, you can have *another* meaning to the / operator in a different
> context, but this aint that context. This discussion is about a/b as
> usually understood in arithmetic.

I just told you how it is understood.

>
>
>>Inverse is a well-defined concept but not
>>necessarily a function, it is a set theoretic mapping. E.G. m/n={ q:
>>m=q*n} by definition, so that m/n which is actually a set which can
>>be empty, a singleton, or infinite.
>
>
> My, my, aint you a clever dude...
>
>
>>In the case of m/n, it is then
>>m/n = F^-1(m) where F(x)= n*x. Your reasoning would lead one to
>>believe /: I x I -> I is a function, which it isn't.
>
>
> Nope. I am using a well understood definition of division as applicable
> to this argument.

Really? You never have told us what your "well understood" definition
is- so what exactly are you "using" here?

```
 0
Reply Fred 12/21/2004 11:12:37 AM

```I read in sci.electronics.design that Kevin Aylward
<salesEXTRACT@anasoft.co.uk> wrote (in <hqTxd.17008\$ef5.10156@fe1.news.b
lueyonder.co.uk>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:

>How can a limit be
>physically meaningfull, yet meaningless?

I don't know, but the word 'meaningless' is meaningful. I hope that is
of no help whatsoever. (;-)
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/21/2004 11:23:21 AM

```On Mon, 20 Dec 2004 21:43:14 +0100, David Kastrup <dak@gnu.org> wrote:

>John Fields <jfields@austininstruments.com> writes:
>
>> On Mon, 20 Dec 2004 09:21:25 -0600, John Sefton <john@petcom.com>
>> wrote:
>>
>>
>>>It's not a prime, because a prime can
>>>only be divided by itself and 1.
>>
>> ---
>> That's not true.  A prime can be divided by anything, but an integer
>> greater than one is prime if its only positive divisors are itself and
>> one, but zero isn't prime because it's even.
>> ---
>>
>>>0 can't be divided by itself,
>>
>> ---
>> Sure it can. Anything (or nothing) divided by itself = 1
>
>Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ?

---
Apparently!

--
John Fields
```
 0
Reply John 12/21/2004 11:53:25 AM

```On Mon, 20 Dec 2004 21:54:18 +0000 (UTC), George Cox
<george_coxanti@spambtinternet.com.invalid> wrote:

>John Fields wrote:
>
>> That's not true.  A prime can be divided by anything, but an integer
>> greater than one is prime if its only positive divisors are itself and
>> one, but zero isn't prime because it's even.
>
>And two isn't prime because it's even?

---
Oops... That's the exception. Sloppy me. :-(

--
John Fields
```
 0
Reply John 12/21/2004 11:59:48 AM

```On Mon, 20 Dec 2004 19:21:43 -0500, Shawn Corey
<shawn.corey@sympatico.ca> wrote:

>Nicholas O. Lindan wrote:
>>
>> 1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2
>>
>
>          a = b
>        a^2 = ab
>  a^2 - b^2 = ab - b^2
>(a+b)(a-b) = b(a-b)
>       a+b  = b
>but a = b
>        a+a = a
>         2a = a
>          2 = 1
>
>What could be clearer?

---

b = 1
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b = b
1+1 = 1

--
John Fields
```
 0
Reply John 12/21/2004 12:16:46 PM

```> >Nicholas O. Lindan wrote:
> >>
> >> 1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2
> >>
> >
> >          a = b
> >        a^2 = ab
> >  a^2 - b^2 = ab - b^2
> >(a+b)(a-b) = b(a-b)

When you attempt to divide by zero, you get...

> >       a+b  = b

Division by zero error!

> >but a = b
> >        a+a = a
> >         2a = a
> >          2 = 1
> >
> >What could be clearer?

Erm, dunno. Glass?

```
 0
Reply Richard 12/21/2004 12:56:50 PM

```"David C. Ullrich" wrote:
>
> On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>
> >Josef Moellers wrote:
> >>
> >> Gactimus wrote:
> >> > I know 0 is neither negative or positive but what about odd/even? I think
> >> > it's even.
> >> >
> >> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> >> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
> >>
> >> As it can be divided by 2 without a remainder, it is obviously even.
> >
> >The divisor would have to be something smaller than 0 like -2.
>
> Huh? 0/2 is somehow undefined because 2 > 0? Interesting.

Well sure. 0 /+N  is illogical. It's like asking:
"How many universes are in a black hole ?"
0/-N makes more sense. Therefore, black holes
have lots of useless anti-matter inside of them. ;-)

>
> >Therefore zero is both even and negative.
> >
> >>
> >> --
> >> Josef M�llers (Pinguinpfleger bei FSC)
> >>         If failure had no penalty success would not be a prize
> >>                                                 -- T.  Pratchett
> >
>
> ************************
>
> David C. Ullrich

```
 0
Reply BB 12/21/2004 2:10:21 PM

```Alfred E. Newman wrote:
> Except for the fact that: 0 / 0 = undefined
> Or actually more correct: n / 0 = undefined

Man, like, we don' need no steenkin' facts ...

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/21/2004 2:38:37 PM

```"David Kastrup" <dak@gnu.org> wrote

> 0/0 is clearly, if anything, a constant expression.  And it turns out
> [to some] that its value is undefined.

Better minds than can be found here have argued this and not reached
any conclusion.  'Undefined' is the answer given by the teacher in the
7th grade, and will serve for all practical purposes.

Maybe what is needed is a New Number = '*' (or something) = Any Number You Want.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

```
 0
Reply Nicholas 12/21/2004 2:43:26 PM

```"BB" <BB@BB.BB> wrote

> "How many universes are in a black hole ?"

Oh, this sounds like even more fun.  Something we know even less

I would say about a black-hole's-worth.

But I don't believe in black holes.

Makes me an expert on the subject ...

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/21/2004 2:46:56 PM

```"Nicholas O. Lindan" wrote:
>
> "BB" <BB@BB.BB> wrote
>
> > "How many universes are in a black hole ?"
>
> Oh, this sounds like even more fun.  Something we know even less

How about some easier questions:

How many black holes are there in the universe ?

Is it meaningful to ask infinity/0 ?

Are we going to need some kind of mathematics
where the second question is somewhat meaningful
in order to answer the first question ?

Is the last (sic) question meaningful ?

>
> I would say about a black-hole's-worth.
>
> But I don't believe in black holes.
>
> Makes me an expert on the subject ...

There are black holes stealing odd socks out of
my laundry.

>
> --
> Nicholas O. Lindan, Cleveland, Ohio
> Consulting Engineer:  Electronics; Informatics; Photonics.
> Remove spaces etc. to reply: n o lindan at net com dot com
> psst.. want to buy an f-stop timer? nolindan.com/da/fstop/

```
 0
Reply BB 12/21/2004 3:20:13 PM

```> >
> > Nope. I am using a well understood definition of division as applicable
> > to this argument.
>
> Really? You never have told us what your "well understood" definition
> is- so what exactly are you "using" here?
>

You guys are arguing two different things.  The argument that 0/0 is the set
of all integers/reals/whatever you are using is the set theory response to
the question.  However, the more commonly used form is the algebraicly
accepted argument that states that division is a function of the forms: Z /
Z -> Q, R / R -> R, etc.  In this definition, division by 0 is undefined for
all Z or R, including 0.  So, you are both correct, but arguing different
things.

```
 0
Reply Richards 12/21/2004 3:39:22 PM

```"Nicholas O. Lindan" <see@sig.com> wrote in message
> "David Kastrup" <dak@gnu.org> wrote
>
> > 0/0 is clearly, if anything, a constant expression.  And it turns out
> > [to some] that its value is undefined.
>
> Better minds than can be found here have argued this and not reached
> any conclusion.  'Undefined' is the answer given by the teacher in the
> 7th grade, and will serve for all practical purposes.
>
> Maybe what is needed is a New Number = '*' (or something) = Any Number You
Want.

Just FYI, if you're performing arithmetic using the IEEE 754 standard, then
n/0 for n not equal to 0 is the infinity with the same sign as n (i.e. -1/0
is -Inf while 1/0 is +Inf).  Under the standard, 0/0 is NaN (Not a Number).
If you scroll down to "Special Operations" on this page:

http://stevehollasch.com/cgindex/coding/ieeefloat.html

you'll see some of the operations on numbers that can be represented in the
form given by the standard that give "special" results.

Professor William Kahan also discusses some of these types of operations in
these lecture notes, starting around page 6:

http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF

--
Steve Lord
slord@mathworks.com

```
 0
Reply Steven 12/21/2004 3:58:07 PM

```"Steven Lord" <slord@mathworks.com> wrote in

> Just FYI, if you're performing arithmetic using the IEEE 754 standard, then
> n/0 for n not equal to ...

Ever hear the one about the Grandmother and blowing eggs?

IEEE passed a standard.  Well, heck then, the issue is settled.
Lets all go home.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/21/2004 4:29:55 PM

```"BB" <BB@BB.BB> wrote

> There are black holes stealing odd socks out of
> my laundry.

No, that's me.

```
 0
Reply Richard 12/21/2004 4:56:40 PM

```Gactimus <gactimus@xrs.net> wrote in news:10sdnunotbnere2@corp.supernews.com:

> I know 0 is neither negative or positive but what about odd/even? I think
> it's even.
>
> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

An even number plus an even number equals an even number.

An odd number plus an even number equals an odd number.

An odd number plus an odd number equals an even number.

0 + 1 = odd number

0 + 2 = even number,  2 is not odd, so zero must be even.

```
 0
Reply Vince 12/21/2004 5:13:53 PM

```<mmeron@cars3.uchicago.edu> wrote in message
news:tURxd.14\$35.4459@news.uchicago.edu...
> In article <32p53dF3paevvU1@individual.net>, "Alfred Z. Newmane"
> <a.newmane.remove@eastcoastcz.com> writes:
>>Nicholas O. Lindan wrote:
>>> "John Sefton" <john@petcom.com> wrote
>>>
>>>> 0 can't be divided by itself,
>>>
>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>
>>> It works if the only three numbers in the universe are
>>> 0, 1, and infinity -- A number system that seems very
>>> suited to usenet.
>>
>>Except for the fact that: 0 / 0 = undefined
>>
>>Or actually more correct: n / 0 = undefined
>>
> The two are not the same.
>
> The definition of the ratio a/b is
>
> a/b = r iff b*r = a
>
> for the case of n/0 there is no r such that r*0 = n (follows from the
> definition of zero.  Therefore n/0 (for non zero n) *does not exist*.
>
> On the other hand, for 0/0, every r qualifies since for every r, r*0 =
> 0 (the definition of zero, again).  Therefore, 0/0 is truly undefined,
> in the sense that it is impossible to *uniquely* assign a value to the
> ratio r.
>
> Mati Meron                      | "When you argue with a fool,
> meron@cars.uchicago.edu         |  chances are he is doing just the same"

It depends on how you get there,  [sin(x)]/x is certainly defined for all
values of x including 0 and infinity.

Tam

```
 0
Reply Tam 12/21/2004 5:44:24 PM

```Tam/WB2TT wrote:

>
> It depends on how you get there,  [sin(x)]/x is certainly defined for all
> values of x including 0 and infinity.
>
> Tam

No, it most certainly is *not*.  [sin(x)]/x for x=0 is
0/0 and is undefined.  The *limit as x approaches 0* of
[sin(x)]/x is 1, but that's not even vaguely the same
thing.  The difference is huge.
--
Christopher Mattern

"Which one you figure tracked us?"
"The ugly one, sir."
"...Could you be more specific?"
```
 0
Reply Chris 12/21/2004 6:34:57 PM

```Alfred Z. Newmane wrote:
> Thats becuase, when translated to reality, that statement becomes (0)^2
> = 0, because 0 has no sign. I really wish people would stop trying to
> spread the false hood that0 actually has a sign.

In the days before IEEE format, at least one FORTRAN was designed to
read, write, and test equality on -0.0, so that it could be used as NaN
(usually for "datum missing"), but I grant that having a real NaN is
ever so much nicer.

--
John W. Kennedy
"I want everybody to be smart. As smart as they can be. A world of
ignorant people is too dangerous to live in."
-- Garson Kanin. "Born Yesterday"
```
 0
Reply John 12/21/2004 7:23:20 PM

```"Fred Bloggs" <nospam@nospam.com> wrote in message
news:41C7FD4F.3060902@nospam.com...
>
>
> David Kastrup wrote:
> > Fred Bloggs <nospam@nospam.com> writes:
> >
> >
> >>Alfred Z. Newmane wrote:
> >>
> >>>Nicholas O. Lindan wrote:
> >>>
> >>>
> >>>>"John Sefton" <john@petcom.com> wrote
> >>>>
> >>>>
> >>>>
> >>>>>0 can't be divided by itself,
> >>>>
> >>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
> >>>>
> >>>>It works if the only three numbers in the universe are
> >>>>0, 1, and infinity -- A number system that seems very
> >>>>suited to usenet.
> >>>
> >>>Except for the fact that: 0 / 0 = undefined
> >>>Or actually more correct: n / 0 = undefined
> >>>
> >>
> >>0/0={ SET OF ALL INTEGERS }
> >>
> >>n/0= NULL SET  for n<>0
> >>
> >>It is very well-defined.
> >
> >
> > So { SET OF ALL INTEGERS } = 0/0 = (0+0)/0 = (2*0)/0 = 2*(0/0)
> >   = 2* {SET OF ALL INTEGERS } = {SET OF ALL EVEN INTEGERS}?
> >
> > Odd.
> >
>
> Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?
>

How about the following:

(2 * 0) / 0  =  (2 * 0) * (1 / 0 )     <-  Definition of division as the
inverse of multiplication
(2 * 0) * (1 / 0) = 2 * (0 * (1 / 0))  <- Associative property of
multiplication
2 * (0 * (1 / 0)) = 2 * (0 / (0 / 1))  <- Definition of division
2 * (0 / (0 / 1)) = 2 * (0 / 0)       <-  0 / 1 = 0

He was just leaving out some unnecessary steps, being as that they are
rather common and generally just understood.

Of course, this is following the same strange assumptions of the fact that 0
/ 0 is a defined operation, or that 0 has an inverse.

```
 0
Reply Richards 12/21/2004 7:28:08 PM

```"Brett Shoelson" <shoelson.no.spam@removethis.helix.nih.gov> wrote in
message news:psGxd.2257\$Ny6.3757@mencken.net.nih.gov...
<SNIP discussions of nada, zip, bupkiss, zilch, goose-egg,....>

> This from Mathworld (http://mathworld.wolfram.com/EvenNumber.html, Eric
> Weisstein's phenomenal online math reference book):
>
> An even number is an integer of the form , where k is an integer. The even
> numbers are therefore ..., -4, -2, 0, 2, 4, 6, 8, 10, ... (Sloane's
> A005843). Since the even numbers are integrally divisible by two, the
> congruence  holds for even n.
>
> Cheers,
> Brett
>
>

Just noticed that the equations didn't copy. Let me try that again:

An even number is an integer of the form n=2k, where k is an integer. The
even
numbers are therefore ..., -4, -2, 0, 2, 4, 6, 8, 10, ... (Sloane's
A005843).
Since the even numbers are integrally divisible by two, the congruence n==0
(mod 2) holds for even n.

Better yet, peruse the site yourself. It is one of the great resources of
the web.
Brett

```
 0
Reply shoelson.no.spam (1038) 12/21/2004 7:39:21 PM

```[huge cross-posting continued remorselessly - fu to rec.puzzles 'cos
that's where I read it]

On Mon, 20 Dec 2004 15:36:15 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

>"John Sefton" <john@petcom.com> wrote
>
>> 0 can't be divided by itself,
>
>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
>It works if the only three numbers in the universe are
>0, 1, and infinity -- A number system that seems very
>suited to usenet.

Someone, and I can't remember who, once said something to the effect
that all computer programs should work like this.  They should allow no
instances of something, one instance of it, or any number at all.

It's not a bad idea - think how many bugs are a result of programs
dealing with far more things than the programmer ever expected.

And let's not, please, have the endless(!) debate about whether infinity
means anything to computers, whether C is a turing complete language
etc.

--
On-line canal route planner: http://www.canalplan.org.uk

(Waterways World site of the month, April 2001)
```
 0
Reply Nick 12/21/2004 8:36:30 PM

```"Tam/WB2TT" <t-tammaru@c0mca\$t.net> wrote in message
news:VK6dnSw-tLV__VXcRVn-jg@comcast.com...
>
> <mmeron@cars3.uchicago.edu> wrote in message
> news:tURxd.14\$35.4459@news.uchicago.edu...
> > In article <32p53dF3paevvU1@individual.net>, "Alfred Z. Newmane"
> > <a.newmane.remove@eastcoastcz.com> writes:
> >>Nicholas O. Lindan wrote:
> >>> "John Sefton" <john@petcom.com> wrote
> >>>
> >>>> 0 can't be divided by itself,
> >>>
> >>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
> >>>
> >>> It works if the only three numbers in the universe are
> >>> 0, 1, and infinity -- A number system that seems very
> >>> suited to usenet.
> >>
> >>Except for the fact that: 0 / 0 = undefined
> >>
> >>Or actually more correct: n / 0 = undefined
> >>
> > The two are not the same.
> >
> > The definition of the ratio a/b is
> >
> > a/b = r iff b*r = a
> >
> > for the case of n/0 there is no r such that r*0 = n (follows from
the
> > definition of zero.  Therefore n/0 (for non zero n) *does not
exist*.
> >
> > On the other hand, for 0/0, every r qualifies since for every r,
r*0 =
> > 0 (the definition of zero, again).  Therefore, 0/0 is truly
undefined,
> > in the sense that it is impossible to *uniquely* assign a value to
the
> > ratio r.
> >
> > Mati Meron                      | "When you argue with a fool,
> > meron@cars.uchicago.edu         |  chances are he is doing just
the same"
>
> It depends on how you get there,  [sin(x)]/x is certainly defined
for all
> values of x including 0 and infinity.

If you knew any maths worth talking about, you would have known that
sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
The first is undefined and the second is unity.

Now it is your turn:  What do you know about sin (infinity) / infinity
?

Franz

```
 0
Reply Franz 12/21/2004 11:20:52 PM

```"Steven Lord" <slord@mathworks.com> wrote in message
news:cq9h6f\$6g8\$1@fred.mathworks.com...
>
> "Nicholas O. Lindan" <see@sig.com> wrote in message
> > "David Kastrup" <dak@gnu.org> wrote
> >
> > > 0/0 is clearly, if anything, a constant expression.  And it
turns out
> > > [to some] that its value is undefined.
> >
> > Better minds than can be found here have argued this and not
reached
> > any conclusion.  'Undefined' is the answer given by the teacher in
the
> > 7th grade, and will serve for all practical purposes.
> >
> > Maybe what is needed is a New Number = '*' (or something) = Any
Number You
> Want.
>
> Just FYI, if you're performing arithmetic using the IEEE 754
standard,

I doubt if there are any mathematicians who care a hoot about
definitions made by engineers for computational convenience

[snip]

Franz

```
 0
Reply Franz 12/21/2004 11:20:53 PM

```"Franz Heymann" <franz.heymann@btopenworld.com> wrote:
> "Steven Lord" <slord@mathworks.com> wrote in message
> news:cq9h6f\$6g8\$1@fred.mathworks.com...
> >
> > "Nicholas O. Lindan" <see@sig.com> wrote in message
> > > "David Kastrup" <dak@gnu.org> wrote
> > >
> > > > 0/0 is clearly, if anything, a constant expression.  And it
> turns out
> > > > [to some] that its value is undefined.
> > >
> > > Better minds than can be found here have argued this and not
> reached
> > > any conclusion.  'Undefined' is the answer given by the teacher in
> the
> > > 7th grade, and will serve for all practical purposes.
> > >
> > > Maybe what is needed is a New Number = '*' (or something) = Any
> Number You
> > Want.
> >
> > Just FYI, if you're performing arithmetic using the IEEE 754
> standard,
>
> I doubt if there are any mathematicians who care a hoot about
> definitions made by engineers for computational convenience
>
> [snip]

Well, then, how about y'all stop crossposting from Hell to breakfast?

Followups set.

Xho

--
Usenet Newsgroup Service                        \$9.95/Month 30GB
```
 0
Reply xhoster 12/21/2004 11:38:19 PM

```In article <VK6dnSw-tLV__VXcRVn-jg@comcast.com>, "Tam/WB2TT" <t-tammaru@c0mca\$t.net> writes:
>
><mmeron@cars3.uchicago.edu> wrote in message
>news:tURxd.14\$35.4459@news.uchicago.edu...
>> In article <32p53dF3paevvU1@individual.net>, "Alfred Z. Newmane"
>> <a.newmane.remove@eastcoastcz.com> writes:
>>>Nicholas O. Lindan wrote:
>>>> "John Sefton" <john@petcom.com> wrote
>>>>
>>>>> 0 can't be divided by itself,
>>>>
>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>
>>>> It works if the only three numbers in the universe are
>>>> 0, 1, and infinity -- A number system that seems very
>>>> suited to usenet.
>>>
>>>Except for the fact that: 0 / 0 = undefined
>>>
>>>Or actually more correct: n / 0 = undefined
>>>
>> The two are not the same.
>>
>> The definition of the ratio a/b is
>>
>> a/b = r iff b*r = a
>>
>> for the case of n/0 there is no r such that r*0 = n (follows from the
>> definition of zero.  Therefore n/0 (for non zero n) *does not exist*.
>>
>> On the other hand, for 0/0, every r qualifies since for every r, r*0 =
>> 0 (the definition of zero, again).  Therefore, 0/0 is truly undefined,
>> in the sense that it is impossible to *uniquely* assign a value to the
>> ratio r.
>>
>> Mati Meron                      | "When you argue with a fool,
>> meron@cars.uchicago.edu         |  chances are he is doing just the same"
>
>It depends on how you get there,  [sin(x)]/x is certainly defined for all
>values of x including 0 and infinity.
>
That's a different thing.  Here you're talking not about a plain value
but a limit (of an infinite set of values).  And this depends how you
get there.  Thus, [sin(0)]/0 is undefined.  On the other hand,
lim_x->0 {[sin[x]/x} is defined and equal to 1.

Mati Meron                      | "When you argue with a fool,
meron@cars.uchicago.edu         |  chances are he is doing just the same"
```
 0
Reply mmeron 12/21/2004 11:39:55 PM

```"Nicholas O. Lindan" schrieb:
> "BB" <BB@BB.BB> wrote
> > "How many universes are in a black hole ?"
>
> Oh, this sounds like even more fun.  Something we know even less
>
> I would say about a black-hole's-worth.

Well, if there's at least one universe inside a black hole, then that
universe could contain another black hole, and so forth.
Because of the Schwarzschild radius, the is at least one universe inside
the black hole separate from ours.
By induction, the answer is: infinitely many.

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/22/2004 12:19:09 AM

```"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
news:cqab4k\$7m1\$6@sparta.btinternet.com...
>
> "Tam/WB2TT" <t-tammaru@c0mca\$t.net> wrote in message
> news:VK6dnSw-tLV__VXcRVn-jg@comcast.com...
>>
>> <mmeron@cars3.uchicago.edu> wrote in message
>> news:tURxd.14\$35.4459@news.uchicago.edu...
>> > In article <32p53dF3paevvU1@individual.net>, "Alfred Z. Newmane"
>> > <a.newmane.remove@eastcoastcz.com> writes:
>> >>Nicholas O. Lindan wrote:
>> >>> "John Sefton" <john@petcom.com> wrote
>> >>>
>> >>>> 0 can't be divided by itself,
>> >>>
>> >>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>> >>>
>> >>> It works if the only three numbers in the universe are
>> >>> 0, 1, and infinity -- A number system that seems very
>> >>> suited to usenet.
>> >>
>> >>Except for the fact that: 0 / 0 = undefined
>> >>
>> >>Or actually more correct: n / 0 = undefined
>> >>
>> > The two are not the same.
>> >
>> > The definition of the ratio a/b is
>> >
>> > a/b = r iff b*r = a
>> >
>> > for the case of n/0 there is no r such that r*0 = n (follows from
> the
>> > definition of zero.  Therefore n/0 (for non zero n) *does not
> exist*.
>> >
>> > On the other hand, for 0/0, every r qualifies since for every r,
> r*0 =
>> > 0 (the definition of zero, again).  Therefore, 0/0 is truly
> undefined,
>> > in the sense that it is impossible to *uniquely* assign a value to
> the
>> > ratio r.
>> >
>> > Mati Meron                      | "When you argue with a fool,
>> > meron@cars.uchicago.edu         |  chances are he is doing just
> the same"
>>
>> It depends on how you get there,  [sin(x)]/x is certainly defined
> for all
>> values of x including 0 and infinity.
>
> If you knew any maths worth talking about, you would have known that
> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
> The first is undefined and the second is unity.
>
Tell that to all the book publishers who print curves for sinx/x.

> Now it is your turn:  What do you know about sin (infinity) / infinity
> ?
>
> Franz
>
>
No problem. Sin x is bounded between +/- 1 for all values of x. A finite
number divided by infinity is 0.

Tam

```
 0
Reply Tam 12/22/2004 12:46:12 AM

```) "Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
) news:cqab4k\$7m1\$6@sparta.btinternet.com...
) <snip>
)> If you knew any maths worth talking about, you would have known that
)> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
)> The first is undefined and the second is unity.

Tam/WB2TT wrote:

) Tell that to all the book publishers who print curves for sinx/x.

If you zoom in on those printed curves far enough, you'll notice that
there is no ink at the actual point (0,1).

SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT
```
 0
Reply Willem 12/22/2004 12:58:55 AM

```"Richards Noah (IFR LIT MET)" <Noah.Richards@infineon.com> wrote

> Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?

The Dorsh Road stop on the #9 line.  But thank you for your
kind and thoughtful response.  You maybe got off a few stops
earlier?

If I treat 0 as an imaginary number, which is what it may
be - what with the way imaginations go wild over the subject,
then 0 <> (2 * 0), as are sqrt(-1) <> 2*sqrt(-1) and
oo <> 2 * oo.

On adding to infinity there is much controversy, some claim

1 + oo <> oo + 1

This gets multiple infinities out of some paradox but is
too bizarre even for me.

There is also a school of thought:

oo < n * oo

Some reject multiplication and claim the next infinity worth

oo = n + oo = n * oo < oo^oo

Infinity, like 0, seems to be imaginary.  Nobody can produce
-nothing-, as nobody can produce -everything-.

But to claim:

n / 0 is illegal and Sister Prudence will rap your knuckles if
you think otherwise.

Well, how petit bourgeois can one get?

Angels and pin-heads anyone?  At least Sister Pru would approve.

*     *     *

Slightly OT, is there an accepted ASCII-gram for square root?

And shouldn't someone add a travel cruise group to the distribution.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 1:56:47 AM

```"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote

> If you knew any maths worth talking about,

I guess in your book I don't, but I won't let that stop me.

> you would have known that
> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.

Gee, and all that analysis I have been doing using sinc(x) as a
test impulse is all wrong: the function is discontinuous and not
differentiable or integrable.  Zeno Rules!

I imagine then that lim(x->2) <> 2.  Makes about much sense to me,
but then I think (2 * 0)/(3 * 0) = 2/3,

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 2:05:46 AM

```<xhoster@gmail.com> wrote in message

> Well, then, how about y'all stop crossposting from Hell to breakfast?

We are being inclusive.  We just got lectured that inclusiveness is a
universal _good thing_, so we are trying it out.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 2:15:00 AM

```Mati Meron <mmeron@cars3.uchicago.edu> wrote

> "When you argue with a fool, chances are he is doing just the same"

I nominate this as the summation of the debate.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 2:19:07 AM

```In article <_D4yd.7692\$Z47.1240@newsread2.news.atl.earthlink.net>,
Nicholas O. Lindan <see@sig.com> wrote:
>"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote
>
>> If you knew any maths worth talking about,
>
>I guess in your book I don't, but I won't let that stop me.
>
>> you would have known that
>> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
>
>Gee, and all that analysis I have been doing using sinc(x) as a
>test impulse is all wrong: the function is discontinuous and not
>differentiable or integrable.  Zeno Rules!

sinc(x) is a useful function that's defined as  sin(pi*x)/pi*x when x
is not equal to 0 and as 1 when x is equal to zero.  But
sin (pi*x)/pi*x is discontinous at zero.

```
 0
Reply russotto 12/22/2004 2:49:08 AM

```I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
'Is zero even or odd?', on Wed, 22 Dec 2004:

>Slightly OT, is there an accepted ASCII-gram for square root?

I've seen v/(x) used; it's fairly evident what it means. I just found
that decimal 175 is an 'overscore' character, �, which means that v/�(x)
could be used.

How about) for cube root?
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/22/2004 4:09:21 AM

```I read in sci.electronics.design that Matthew Russotto
<russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>But sin (pi*x)/pi*x is
>discontinous at zero.

Is it? Does the limit of its differential differ as x->0+ and as x->0-?
If not, it's 'squeezed'.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/22/2004 4:13:27 AM

```I read in sci.electronics.design that John Woodgate <jmw@jmwa.demon.cont
raspam.yuk> wrote (in <XNLAFxBxNPyBFw88@jmwa.demon.co.uk>) about 'Is
zero even or odd?', on Wed, 22 Dec 2004:

>How about) for cube root?

My newsreader jibbed at that, as you can see, so yours may have, too. It
had the exponent-3 character, decimal 179, before the v/�(x) group.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/22/2004 4:31:14 AM

```On Wed, 22 Dec 2004 01:56:47 +0000, Nicholas O. Lindan wrote:

> Slightly OT,

Only slightly?

> is there an accepted ASCII-gram for square root?

_______
_                              /(x+y)*z
v2 would be my suggestion, or  / ------- for more complex expressions.
v    a+2

sqrt(2) or 2^.5 is generally more manageable, though.

> And shouldn't someone add a travel cruise group to the distribution.

*scratches head* *googles* Ah, there's a cruise line named Infinity.

```
 0
Reply Ed 12/22/2004 4:44:35 AM

```On Mon, 20 Dec 2004 14:21:11 -0000, Gactimus <gactimus@xrs.net> wrote:

>Subject: Is zero even or odd?

Yes it is!

Michele
--
{\$_=pack'B8'x25,unpack'A8'x32,\$a^=sub{pop^pop}->(map substr
((\$a||=join'',map--\$|x\$_,(unpack'w',unpack'u','G^<R<Y]*YB='
..'KYU;*EVH[.FHF2W+#"\Z*5TI/ER<Z`S(G.DZZ9OX0Z')=~/./g)x2,\$_,
256),7,249);s/[^\w,]/ /g;\$ \=/^J/?\$/:"\r";print,redo}#JAPH,
```
 0
Reply Michele 12/22/2004 7:33:26 AM

```John Woodgate schrieb:
> I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
>
> >Slightly OT, is there an accepted ASCII-gram for square root?
>
> I've seen v/(x) used; it's fairly evident what it means. I just found
> that decimal 175 is an 'overscore' character, �, which means that v/�(x)
> could be used.

I suggest

�v�(a+b) = v�(a+b) = (a+b)^(1/2) = (a+b)^� = sqrt(a+b)

�v�(a+b) = (a+b)^(1/3)

The ASCII-grams have the worst readability of the bunch, IMO.

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/22/2004 8:23:58 AM

```Willem <willem@stack.nl> writes:

> ) "Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
> ) news:cqab4k\$7m1\$6@sparta.btinternet.com...
> ) <snip>
> )> If you knew any maths worth talking about, you would have known that
> )> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
> )> The first is undefined and the second is unity.
>
> Tam/WB2TT wrote:
>
> ) Tell that to all the book publishers who print curves for sinx/x.
>
> If you zoom in on those printed curves far enough, you'll notice
> that there is no ink at the actual point (0,1).

Exactly at 0 (and nowhere else), there is a vertical smear from
roadkill.  If you ever wondered where Schr�dinger's cat ended up after
all, this is it.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/22/2004 10:11:19 AM

```Ed Murphy <emurphy42@socal.rr.com> writes:

> On Wed, 22 Dec 2004 01:56:47 +0000, Nicholas O. Lindan wrote:
>
>> Slightly OT,
>
> Only slightly?
>
>> is there an accepted ASCII-gram for square root?
>
>                                  _______
>  _                              /(x+y)*z
> v2 would be my suggestion, or  / ------- for more complex expressions.
>                               v    a+2
>
> sqrt(2) or 2^.5 is generally more manageable, though.

Well Emacs Calc suggests

___________
| (x + y) z
| ---------
\|   a + 2

and there is something to be said for your Usenet reader to be able to
manipulate simple formulas graphically.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/22/2004 10:18:24 AM

```Richard S Beckett wrote:
>>>Nicholas O. Lindan wrote:
>>>
>>>>1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2
>>>>
>>>
>>>         a = b
>>>       a^2 = ab
>>> a^2 - b^2 = ab - b^2
>>>(a+b)(a-b) = b(a-b)
>
>
> When you attempt to divide by zero, you get...
>
>
>>>      a+b  = b
>
>
> Division by zero error!
>
>
>>>but a = b
>>>       a+a = a
>>>        2a = a

You missed one. The above implies a=0 therefore the next statement also
divides by zero.

>>>         2 = 1
>>>
>>>What could be clearer?
>
>
> Erm, dunno. Glass?
>
>
Don't you know sarcasm when you hear it?

--- Shawn
```
 0
Reply Shawn 12/22/2004 12:18:34 PM

```"Gactimus" wrote:
> I know 0 is neither negative or positive but what about odd/even? I think
> it's even.

Of course it is.  There exists a whole number X such that X*2=0.  Thus, 0 is
even.

Bill Smythe

```
 0
Reply Bill 12/22/2004 1:23:14 PM

```On Mon, 20 Dec 2004 15:24:39 +0100, Josef Moellers
<josef.moellers@fujitsu-siemens.com> wrote:

>Gactimus wrote:
>> I know 0 is neither negative or positive but what about odd/even? I think
>> it's even.
>>
>> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>
>As it can be divided by 2 without a remainder, it is obviously even.

Er..., it can also be divided by every other number (rational,
irrational, and imaginary) without a remainder, although some of us
are amused by the strange concept of dividing nothing and the absurd
idea that there may be a `remainder'. Then comes the wild assertion
that when a number is divided by nothing, it becomes infinite.
```
 0
Reply vonroach 12/22/2004 1:56:07 PM

```On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:

>The divisor would have to be something smaller than 0 like -2.
>Therefore zero is both even and negative.

Whoa!  A new concept: -0.  Let's make up some other numbers. I suggest
wizzad and fugawe. I'd have suggested Arunda, but I believe some
obscure African group already uses that in their alphabet.
```
 0
Reply vonroach 12/22/2004 2:04:15 PM

```On 20 Dec 2004 07:02:45 -0800, merlyn@stonehenge.com (Randal L.
Schwartz) wrote:

>This is a troll.   *Negative*?  Can I have some of the drug you're
>smoking? :)

That's no good Randy, no matter how much you buy, you still have
nothing. Coincidentally with constant use the measurable IQ approaches
zero as a limit.
```
 0
Reply vonroach 12/22/2004 2:08:44 PM

```On Mon, 20 Dec 2004 09:21:25 -0600, John Sefton <john@petcom.com>
wrote:

>Randal L. Schwartz wrote:
>>>>>>>"BB" == BB  <BB@BB.BB> writes:
>>>>>>
>>
>> BB> The divisor would have to be something smaller than 0 like -2.
>> BB> Therefore zero is both even and negative.
>>
>> This is a troll.   *Negative*?  Can I have some of the drug you're
>> smoking? :)
>>
>
>It's not a prime, because a prime can
>only be divided by itself and 1.
>0 can't be divided by itself, but
>can be divided by everything else.
>An anti-prime?
>John
Perhaps a superprime. `antiprime' is as mysterious as - 0.
```
 0
Reply vonroach 12/22/2004 2:12:02 PM

```"Shawn Corey" <shawn.corey@sympatico.ca> wrote

> >>>What could be clearer?
> > Erm, dunno. Glass?
> Don't you know sarcasm when you hear it?

Nope! ;-)

```
 0
Reply Richard 12/22/2004 2:14:13 PM

```On Mon, 20 Dec 2004 15:36:15 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

>"John Sefton" <john@petcom.com> wrote
>
>> 0 can't be divided by itself,
>
>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
>It works if the only three numbers in the universe are
>0, 1, and infinity -- A number system that seems very
>suited to usenet.
Add to that the troubling thought that 1/0, 1/1, 0/1, and 0/0 are all
rational numbers. If 1/0 = `infinity' how do we decide if there is any
remainder? Looks like there should be a remainder of 1. If that is so,
how do we know it has really been divided by 0?
```
 0
Reply vonroach 12/22/2004 2:19:44 PM

```On Mon, 20 Dec 2004 22:19:46 +0000 (UTC), "Franz Heymann"
<notfranz.heymann@btopenworld.com> wrote:

>There is no lack of rigour in the definition of infinity.  Read anbout
>the work of Cantor, Dedekind and others.

Do you have similar `readings' covering 0?
```
 0
Reply vonroach 12/22/2004 2:24:59 PM

```On Mon, 20 Dec 2004 15:43:59 -0500, Shawn Corey
<shawn.corey@sympatico.ca> wrote:

>Nicholas O. Lindan wrote:
>> "John Sefton" <john@petcom.com> wrote
>>
>>
>>>0 can't be divided by itself,
>>
>>
>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>
>> It works if the only three numbers in the universe are
>> 0, 1, and infinity -- A number system that seems very
>> suited to usenet.
>>
>
>Zero is even. You cannot divide by zero. Limits are not division.
>Infinity is not a number. Computers bugger up the system.
>
>    --- Shawn
Shawn, I am equally convinced that it is neither even or odd. Though I
will admit that those who need to decide are rather odd.
```
 0
Reply vonroach 12/22/2004 2:27:48 PM

```On Mon, 20 Dec 2004 15:21:14 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:

>Except for the fact that: 0 / 0 = undefined
>
>Or actually more correct: n / 0 = undefined

Really, Al Z?  Where did you get that doctorate in math? Various
middle eastern types have worked hard to see that was not the case.
```
 0
Reply vonroach 12/22/2004 2:33:47 PM

```On Tue, 21 Dec 2004 01:08:55 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

>
>
>Alfred Z. Newmane wrote:
>> Nicholas O. Lindan wrote:
>>
>>>"John Sefton" <john@petcom.com> wrote
>>>
>>>
>>>>0 can't be divided by itself,
>>>
>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>
>>>It works if the only three numbers in the universe are
>>>0, 1, and infinity -- A number system that seems very
>>>suited to usenet.
>>
>>
>> Except for the fact that: 0 / 0 = undefined
>>
>> Or actually more correct: n / 0 = undefined
>>
>>
>
>0/0={ SET OF ALL INTEGERS }
>
>n/0= NULL SET  for n<>0

Why drag n <>0 into an otherwise friendly discussion.

>It is very well-defined.

```
 0
Reply vonroach 12/22/2004 2:35:54 PM

```On Tue, 21 Dec 2004 07:08:11 GMT, "Kevin Aylward"
<salesEXTRACT@anasoft.co.uk> wrote:

>Fred Bloggs wrote:
>> Alfred Z. Newmane wrote:
>>> Nicholas O. Lindan wrote:
>>>
>>>> "John Sefton" <john@petcom.com> wrote
>>>>
>>>>
>>>>> 0 can't be divided by itself,
>>>>
>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>
>>>> It works if the only three numbers in the universe are
>>>> 0, 1, and infinity -- A number system that seems very
>>>> suited to usenet.
>>>
>>>
>>> Except for the fact that: 0 / 0 = undefined
>>>
>>> Or actually more correct: n / 0 = undefined
>>>
>>>
>>
>> 0/0={ SET OF ALL INTEGERS }
>
>No.
>
>>
>> n/0= NULL SET  for n<>0
>>
>> It is very well-defined.
>
>No it isnt.
>
>Kevin Aylward
Now that you are in to definitions, what does `Aylward' mean?

```
 0
Reply vonroach 12/22/2004 2:38:20 PM

```On Tue, 21 Dec 2004 10:37:35 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

>
>
>Kevin Aylward wrote:
>> Fred Bloggs wrote:
>>
>>>Alfred Z. Newmane wrote:
>>>
>>>>Nicholas O. Lindan wrote:
>>>>
>>>>
>>>>>"John Sefton" <john@petcom.com> wrote
>>>>>
>>>>>
>>>>>
>>>>>>0 can't be divided by itself,
>>>>>
>>>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>
>>>>>It works if the only three numbers in the universe are
>>>>>0, 1, and infinity -- A number system that seems very
>>>>>suited to usenet.
>>>>
>>>>
>>>>Except for the fact that: 0 / 0 = undefined
>>>>
>>>>Or actually more correct: n / 0 = undefined
>>>>
>>>>
>>>
>>>0/0={ SET OF ALL INTEGERS }
>>
>>
>> No.
>>
>>
>>>n/0= NULL SET  for n<>0
>>>
>>>It is very well-defined.
>>
>>
>> No it isnt.
>>
>> Kevin Aylward
>
>You apparently have stumbled on something else you know damn little
>about. In case you need help with this , you might note that "/" is NOT
>an operator on the integers, it is the "inverse" of a multiplication
>operator. Inverse is a well-defined concept but not necessarily a
>function, it is a set theoretic mapping. E.G. m/n={ q: m=q*n} by
>definition, so that m/n which is actually a set which can be empty, a
>singleton, or infinite. In the case of m/n, it is then m/n = F^-1(m)
>where F(x)= n*x. Your reasoning would lead one to believe /: I x I -> I
>is a function, which it isn't.

Ah, the inverse , like 1/0 is inverse of 0/1?  Is 0/0 the inverse of
0/0? And 1/1, the inverse of 1/1.
```
 0
Reply vonroach 12/22/2004 2:43:11 PM

```On Tue, 21 Dec 2004 11:04:59 GMT, "Kevin Aylward"
<salesEXTRACT@anasoft.co.uk> wrote:

>Sure, you can have *another* meaning to the / operator in a different
>context, but this aint that context. This discussion is about a/b as
>usually understood in arithmetic.

a/b ? Now your getting into complicated stuff.
```
 0
Reply vonroach 12/22/2004 2:46:31 PM

```On Tue, 21 Dec 2004 10:40:32 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

>Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?

(2 x0)/0 = 2x(0/0)  . there now is that better?
```
 0
Reply vonroach 12/22/2004 2:54:12 PM

```On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

>If I treat 0 as an imaginary number

Now you say 0= -1^1/2?  You are using your imagination.
```
 0
Reply vonroach 12/22/2004 2:58:35 PM

```I read in sci.electronics.design that Franz Heymann <notfranz.heymann@bt
openworld.com> wrote (in <cq7j61\$6gm\$2@sparta.btinternet.com>) about 'Is
zero even or odd?', on Mon, 20 Dec 2004:
>There is no lack of rigour in the definition of infinity.  Read anbout
>the work of Cantor, Dedekind and others.

Indeed: I was referring to the lack of rigour in '1/0 = infinity'.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/22/2004 2:59:18 PM

```"vonroach" <hadrainc@earthlink.net> wrote
> On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
> >If I treat 0 as an imaginary number
> Now you say 0= -1^1/2?  You are using your imagination.

No, I think you are the first to say that, at least in this thread.

There are more imaginary numbers in the usenet than are counted

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 3:17:40 PM

```
vonroach wrote:

> Er..., it can also be divided by every other number (rational,
> irrational, and imaginary) without a remainder,

irrelevent. The -definition- of an even integer is an integer equivalent
to zero mod 2. Given any integer k != 0 we can always find an even
multiple of k. We can also find an odd multiple of k.

Bob Kolker
```
 0
Reply robert 12/22/2004 3:32:46 PM

```vonroach <hadrainc@earthlink.net> writes:

> On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
> wrote:
>
>>If I treat 0 as an imaginary number
>
> Now you say 0= -1^1/2?  You are using your imagination.

0 is even, but not odd, but it is _both_ a purely real and a purely
imaginary number.  And it is the _only_ number that manages that feat.

Like f(x)=0 is the only function that manages the feat to be at the
same time an even and an odd function.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/22/2004 3:44:43 PM

```vonroach wrote:
> On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>
>> The divisor would have to be something smaller than 0 like -2.
>> Therefore zero is both even and negative.
>
> Whoa!  A new concept: -0.  Let's make up some other numbers. I suggest
> wizzad and fugawe. I'd have suggested Arunda, but I believe some
> obscure African group already uses that in their alphabet.

-0 often/usually signifies a limit approaching from the negative
direction.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/22/2004 3:51:57 PM

```vonroach wrote:
> On Tue, 21 Dec 2004 07:08:11 GMT, "Kevin Aylward"
> <salesEXTRACT@anasoft.co.uk> wrote:
>
>> Fred Bloggs wrote:
>>> Alfred Z. Newmane wrote:
>>>> Nicholas O. Lindan wrote:
>>>>
>>>>> "John Sefton" <john@petcom.com> wrote
>>>>>
>>>>>
>>>>>> 0 can't be divided by itself,
>>>>>
>>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>
>>>>> It works if the only three numbers in the universe are
>>>>> 0, 1, and infinity -- A number system that seems very
>>>>> suited to usenet.
>>>>
>>>>
>>>> Except for the fact that: 0 / 0 = undefined
>>>>
>>>> Or actually more correct: n / 0 = undefined
>>>>
>>>>
>>>
>>> 0/0={ SET OF ALL INTEGERS }
>>
>> No.
>>
>>>
>>> n/0= NULL SET  for n<>0
>>>
>>> It is very well-defined.
>>
>> No it isnt.
>>
>> Kevin Aylward
> Now that you are in to definitions, what does `Aylward' mean?

"Warden of the King's Ale"

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/22/2004 3:52:43 PM

```"Kevin Aylward" <salesEXTRACT@anasoft.co.uk> writes:
> vonroach wrote:
> > On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
> >
> >> The divisor would have to be something smaller than 0 like -2.
> >> Therefore zero is both even and negative.
> >
> > Whoa!  A new concept: -0.  Let's make up some other numbers. I suggest
> > wizzad and fugawe. I'd have suggested Arunda, but I believe some
> > obscure African group already uses that in their alphabet.
>
> -0 often/usually signifies a limit approaching from the negative
> direction.

And in computing, there are representations of integers in binary that
have both a 0 and a -0. Of floating-point too, for that matter.
```
 0
Reply Arndt 12/22/2004 3:59:55 PM

```Kevin Aylward wrote:

>
> "Warden of the King's Ale"
>

You wish! It's more like one of these almost production- line
mix-and-match names that the Anglo-Saxons went in for, you know,
ethelfrith, ethelred, brithnoth, brithelm etc. etc. I'd guess it means
something like "noble guard". They quite often got abraded over time-
Wolverton being Wulfheardestun or similar, so the change in sound isn't
surprising. Put it down to the Great Bowel Shift.

Paul Burke
```
 0
Reply Paul 12/22/2004 4:06:54 PM

```
Arndt Jonasson wrote:
>
> And in computing, there are representations of integers in binary that
> have both a 0 and a -0. Of floating-point too, for that matter.

Forr that matters not. Finite representations of numbers are an artifact
of the computer memory and have little to do with the numbers themselves.

Bob Kolker
```
 0
Reply robert 12/22/2004 4:15:10 PM

```"Kevin Aylward" <salesEXTRACT@anasoft.co.uk> writes:

> vonroach wrote:
>> On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>>
>>> The divisor would have to be something smaller than 0 like -2.
>>> Therefore zero is both even and negative.
>>
>> Whoa!  A new concept: -0.  Let's make up some other numbers. I suggest
>> wizzad and fugawe. I'd have suggested Arunda, but I believe some
>> obscure African group already uses that in their alphabet.
>
> -0 often/usually signifies a limit approaching from the negative
> direction.

No.  One writes 0- for that.  As in

lim     exp(1/x) = 0
x -> 0-

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/22/2004 4:18:49 PM

```"robert j. kolker" <nowhere@nowhere.net> writes:
> Arndt Jonasson wrote:
> > And in computing, there are representations of integers in binary
> > that
> > have both a 0 and a -0. Of floating-point too, for that matter.
>
> Forr that matters not. Finite representations of numbers are an
> artifact of the computer memory and have little to do with the numbers
> themselves.

You may not have noticed, but this discussion has already entered the
free association phase.

My CD player also has a -0. When it shows the number of seconds played
on a track, it sometimes starts with a negative number and goes -2 -1
-0 0 1 2 ...  There is a full second between -0 and 0.
(sci.electronics.design, why not.)
```
 0
Reply Arndt 12/22/2004 4:26:05 PM

```Fred Bloggs wrote:
> Kevin Aylward wrote:
>> Fred Bloggs wrote:
>>
>>> Alfred Z. Newmane wrote:
>>>
>>>> Nicholas O. Lindan wrote:
>>>>
>>>>
>>>>> "John Sefton" <john@petcom.com> wrote
>>>>>
>>>>>
>>>>>
>>>>>> 0 can't be divided by itself,
>>>>>
>>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>
>>>>> It works if the only three numbers in the universe are
>>>>> 0, 1, and infinity -- A number system that seems very
>>>>> suited to usenet.
>>>>
>>>>
>>>> Except for the fact that: 0 / 0 = undefined
>>>>
>>>> Or actually more correct: n / 0 = undefined
>>>>
>>>>
>>>
>>> 0/0={ SET OF ALL INTEGERS }
>>
>>
>> No.
>>
>>
>>> n/0= NULL SET  for n<>0
>>>
>>> It is very well-defined.
>>
>>
>> No it isnt.
>>
>> Kevin Aylward
>
> You apparently have stumbled on something else you know damn little
> about. In case you need help with this , you might note that "/" is
> NOT an operator on the integers, it is the "inverse" of a
> multiplication operator. Inverse is a well-defined concept but not
> necessarily a function, it is a set theoretic mapping. E.G. m/n={ q:
> m=q*n} by definition, so that m/n which is actually a set which can
> be empty, a singleton, or infinite. In the case of m/n, it is then
> m/n = F^-1(m) where F(x)= n*x. Your reasoning would lead one to
> believe /: I x I -> I is a function, which it isn't.

Then why can you not perform 1/0 ? (or n/0)

Error: DIV BY ZERO

```
 0
Reply Alfred 12/22/2004 5:26:48 PM

```David Kastrup wrote:
> Fred Bloggs <nospam@nospam.com> writes:
>
>> Alfred Z. Newmane wrote:
>>> Nicholas O. Lindan wrote:
>>>
>>>> "John Sefton" <john@petcom.com> wrote
>>>>
>>>>
>>>>> 0 can't be divided by itself,
>>>>
>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>
>>>> It works if the only three numbers in the universe are
>>>> 0, 1, and infinity -- A number system that seems very
>>>> suited to usenet.
>>> Except for the fact that: 0 / 0 = undefined
>>> Or actually more correct: n / 0 = undefined
>>>
>>
>> 0/0={ SET OF ALL INTEGERS }
>>
>> n/0= NULL SET  for n<>0
>>
>> It is very well-defined.
>
> So { SET OF ALL INTEGERS } = 0/0 = (0+0)/0 = (2*0)/0 = 2*(0/0)
>   = 2* {SET OF ALL INTEGERS } = {SET OF ALL EVEN INTEGERS}?
>
> Odd.

Thanks for pointing this out. n/0 = undefined. It's never been "SET OF
ALL INT'S"; though in basic math classses they do teach that it IS null
set, though the most correct and universal answer is simply n/0 =
undefined.

```
 0
Reply Alfred 12/22/2004 5:35:24 PM

```vonroach wrote:
> On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
> wrote:
>
>> If I treat 0 as an imaginary number
>
> Now you say 0= -1^1/2?  You are using your imagination.

Sorry to nit pick, but in most any proper clac it should be written as
(-1)^(1/2), less you get -1 from -1^1/2, due to the '-' being evaluated
last. At least thats what happens in my TI86.

```
 0
Reply Alfred 12/22/2004 5:45:20 PM

```Tam/WB2TT wrote:
> <mmeron@cars3.uchicago.edu> wrote in message
> news:tURxd.14\$35.4459@news.uchicago.edu...
>> In article <32p53dF3paevvU1@individual.net>, "Alfred Z. Newmane"
>> <a.newmane.remove@eastcoastcz.com> writes:
>>> Nicholas O. Lindan wrote:
>>>> "John Sefton" <john@petcom.com> wrote
>>>>
>>>>> 0 can't be divided by itself,
>>>>
>>>> Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>
>>>> It works if the only three numbers in the universe are
>>>> 0, 1, and infinity -- A number system that seems very
>>>> suited to usenet.
>>>
>>> Except for the fact that: 0 / 0 = undefined
>>>
>>> Or actually more correct: n / 0 = undefined
>>>
>> The two are not the same.
>>
>> The definition of the ratio a/b is
>>
>> a/b = r iff b*r = a
>>
>> for the case of n/0 there is no r such that r*0 = n (follows from the
>> definition of zero.  Therefore n/0 (for non zero n) *does not exist*.
>>
>> On the other hand, for 0/0, every r qualifies since for every r, r*0
>> = 0 (the definition of zero, again).  Therefore, 0/0 is truly
>> undefined, in the sense that it is impossible to *uniquely* assign a
>> value to the ratio r.
>>
>> Mati Meron                      | "When you argue with a fool,
>> meron@cars.uchicago.edu         |  chances are he is doing just the
>> same"
>
> It depends on how you get there,  [sin(x)]/x is certainly defined for
> all values of x including 0 and infinity.

Am I missing something here? you're still DIVIDING, so when x = 0, the
result is undefined.

```
 0
Reply Alfred 12/22/2004 5:48:57 PM

```vonroach wrote:
> On Mon, 20 Dec 2004 15:21:14 -0800, "Alfred Z. Newmane"
> <a.newmane.remove@eastcoastcz.com> wrote:
>
>> Except for the fact that: 0 / 0 = undefined
>>
>> Or actually more correct: n / 0 = undefined
>
> Really, Al Z?  Where did you get that doctorate in math? Various
> middle eastern types have worked hard to see that was not the case.

Did you have a refutal somewhere?

```
 0
Reply Alfred 12/22/2004 5:55:02 PM

```On Wed, 22 Dec 2004 13:56:07 GMT, vonroach <hadrainc@earthlink.net>
wrote:

>On Mon, 20 Dec 2004 15:24:39 +0100, Josef Moellers
><josef.moellers@fujitsu-siemens.com> wrote:
>
>>Gactimus wrote:
>>> I know 0 is neither negative or positive but what about odd/even? I think
>>> it's even.
>>>
>>> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>>> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>
>>As it can be divided by 2 without a remainder, it is obviously even.
>
>Er..., it can also be divided by every other number (rational,
>irrational, and imaginary) without a remainder, although some of us
>are amused by the strange concept of dividing nothing and the absurd
>idea that there may be a `remainder'. Then comes the wild assertion
>that when a number is divided by nothing, it becomes infinite.

---
???

For

1
x = ---
n

x grows without bound as n approaches zero, no?

--
John Fields
```
 0
Reply John 12/22/2004 6:01:43 PM

```John Fields wrote:
> On Wed, 22 Dec 2004 13:56:07 GMT, vonroach <hadrainc@earthlink.net>
> wrote:
>
>> On Mon, 20 Dec 2004 15:24:39 +0100, Josef Moellers
>> <josef.moellers@fujitsu-siemens.com> wrote:
>>
>>> Gactimus wrote:
>>>> I know 0 is neither negative or positive but what about odd/even?
>>>> I think it's even.
>>>>
>>>> Odd numbers start at 1 and go every other number
>>>> 1,3,5,7;1,-1,-3,-5,-7 Even starts at 2 and go every other number
>>>> 2,4,6,8;2,0,-2,-4,-6,-8
>>>
>>> As it can be divided by 2 without a remainder, it is obviously even.
>>
>> Er..., it can also be divided by every other number (rational,
>> irrational, and imaginary) without a remainder, although some of us
>> are amused by the strange concept of dividing nothing and the absurd
>> idea that there may be a `remainder'. Then comes the wild assertion
>> that when a number is divided by nothing, it becomes infinite.
>
> ---
> ???
>
> For
>
>              1
>         x = ---
>              n
>
> x grows without bound as n approaches zero, no?

Exactly: graph y = 1 / x

You get a graph that loos like this:
(Both the  ---- line and the horizontal segments of ... are y = 0, drawn
as such since to show what the graph line looks like without being
overlapped by the origin (zero point) line.)

y = 1 / x:

| (doesn't quite reach 0,
|.  <--  since y = undefiend for x = 0)
|.
| ..
(<- etc) .......   |   ....... (etc ->)
-------..-+----------
.|
-->  .|
(doesn't quite  |
reach 0, since y = undefiend for x = 0)

```
 0
Reply Alfred 12/22/2004 6:30:37 PM

```David Kastrup wrote:
> "Kevin Aylward" <salesEXTRACT@anasoft.co.uk> writes:
>
>> vonroach wrote:
>>> On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>>>
>>>> The divisor would have to be something smaller than 0 like -2.
>>>> Therefore zero is both even and negative.
>>>
>>> Whoa!  A new concept: -0.  Let's make up some other numbers. I
>>> suggest wizzad and fugawe. I'd have suggested Arunda, but I believe
>>> some obscure African group already uses that in their alphabet.
>>
>> -0 often/usually signifies a limit approaching from the negative
>> direction.
>
> No.  One writes 0- for that.

Your quibbling here, smart arse.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/22/2004 6:35:20 PM

```
Alfred Z. Newmane wrote:

>
> Then why can you not perform 1/0 ? (or n/0)

If n/0 for n not 0 had a value then it would be equal to 0 and not equal
to 0 at the same time. Contradictions are not permitted.

Bob Kolker
```
 0
Reply robert 12/22/2004 6:59:13 PM

```On Wed, 22 Dec 2004 11:18:24 +0100, David Kastrup <dak@gnu.org> wrote,
in part:
>Ed Murphy <emurphy42@socal.rr.com> writes:
>> On Wed, 22 Dec 2004 01:56:47 +0000, Nicholas O. Lindan wrote:
>>
>>> Slightly OT,
>>
>> Only slightly?
>>
>>> is there an accepted ASCII-gram for square root?
>>
>>                                  _______
>>  _                              /(x+y)*z
>> v2 would be my suggestion, or  / ------- for more complex expressions.
>>                               v    a+2
>>
>> sqrt(2) or 2^.5 is generally more manageable, though.
>
>Well Emacs Calc suggests
>
>  ___________
> | (x + y) z
> | ---------
>\|   a + 2
>
>and there is something to be said for your Usenet reader to be able to
>manipulate simple formulas graphically.

I like the first form visually, but I do feel that it can be confusing
to use letters anywhere in a built-up portion of a formula, so my choice
is:

_____________
/  (x + y) z
/  -----------
\/      a + 2

I found that one easy enough; where I had to think a bit was to find a
good substitute for the integral sign:

_
/  p     2
|        x + 4x + 3
|       ------------ , dx
|           x + 1
_/  0

That, I think, would scale well to larger sizes. Thus, we can have

_
/  theta         /  psi     pi \         /  psi     pi \
|            sin |  ----- + ---  | + cos |  ----- + ---  |
|                 \   2      4  /         \   2      4  /
|          ------------------------------------------------- , d psi
|                       ____________________________
|                      /        2  /  psi     pi \
|                     /  1 + tan  |  ----- - ---  |
_/  0                 \/             \   2      4  /

John Savard
http://home.ecn.ab.ca/~jsavard/index.html
```
 0
Reply jsavard 12/22/2004 7:10:39 PM

```"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote

> Sorry to nit pick, but in most any proper clac it should be written as
> (-1)^(1/2), less you get -1 from -1^1/2, due to the '-' being evaluated
> last. At least thats what happens in my TI86.

That's the problem here.  Folks are using the wrong calculator.

On an hp49 (physically a horrible peice of junk, now made by
Casio(?), don't buy one) there is at least an 'oo' key.

It complains about oo when 1^0/ is _entered_, but it happily
uses 10^500 when it comes time to numerically evaluate oo.

Those for who Reversed not their Polish is 1^0/ is an
asciigram for '1 [enter] 0 [divide]'

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 7:19:47 PM

```"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote

> Am I missing something here?
No, not really - nobody has said anything profound yet.

> you're still DIVIDING [by 0],
The nub of the matter for sure.  If we stopped this thread
would cease to be.

> so when x = 0, the result [1/x] is undefined.

Well, we sure can't find a definition.

It is, in truth, 'arguably undefined'.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 7:25:31 PM

```vonroach <hadrainc@earthlink.net> writes:

> On Mon, 20 Dec 2004 15:24:39 +0100, Josef Moellers
> <josef.moellers@fujitsu-siemens.com> wrote:
>
>>Gactimus wrote:
>>> I know 0 is neither negative or positive but what about odd/even? I think
>>> it's even.
>>>
>>> Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
>>> Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>>
>>As it can be divided by 2 without a remainder, it is obviously even.
>
> Er..., it can also be divided by every other number (rational,
> irrational, and imaginary) without a remainder,

Which means that it is also a multiple of 3, 4, 5, 6...  against which
there is no law.  It does make 0 the center of the additive universe.

> although some of us are amused by the strange concept of dividing
> nothing and the absurd idea that there may be a `remainder'. Then
> comes the wild assertion that when a number is divided by nothing,
> it becomes infinite.

Numbers don't become, they are.  4 does not "become" 2 if I divide it
by 2.  Half of 4 _is_ 2.

And if I divide 1 by 0, the related question is "if I have one piece
of candy, and I hand out equal amounts of candy to nobody until there
is no candy left, ..."  Bzzzzt.  No need to look further.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
```
 0
Reply David 12/22/2004 8:02:12 PM

```Kevin Aylward wrote:
> vonroach wrote:
>
>>On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>>
>>
>>>The divisor would have to be something smaller than 0 like -2.
>>>Therefore zero is both even and negative.
>>
>>Whoa!  A new concept: -0.  Let's make up some other numbers. I suggest
>>wizzad and fugawe. I'd have suggested Arunda, but I believe some
>>obscure African group already uses that in their alphabet.
>
>
> -0 often/usually signifies a limit approaching from the negative
> direction.

But that is an indication of direction to approach from, NOT a sign on
the zero. When approaching f(x) from -0, we are not somehow computing
with "negative zero".
So while "-0" may have a defined meaning, it is certainly not
"negative zero".
This is getting too silly.

kwallace

>
> Kevin Aylward
> salesEXTRACT@anasoft.co.uk
> http://www.anasoft.co.uk
> SuperSpice, a very affordable Mixed-Mode
> Windows Simulator with Schematic Capture,
> Waveform Display, FFT's and Filter Design.
>
>
```
 0
Reply k 12/22/2004 8:11:48 PM

```"robert j. kolker" <nowhere@nowhere.net> wrote

> > Then why can you not perform 1/0 ? (or n/0)
>
> If n/0 for n not 0 had a value then it would be equal to 0 and not equal
> to 0 at the same time.

???

The common contrarian take is:

1 / 0 = oo
n / 0 = n * oo
0 / 0 = 0 * oo = 1

I take the stance that 0 and oo are imaginary and sticky.  Once
you have an equation with a 0 in it you are stuck with the zero.

2 * 0 == 0 + 0 and it doesn't simplify

As doesn't

2 * sqrt(-1) = sqrt(-1) + sqrt(-1)

> Contradictions are not permitted.

Who made that up?

Anyway, I am of contradictions, they were taken out and
slapped across my brow several days ago.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 8:46:33 PM

```On Wed, 22 Dec 2004 10:30:37 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:

>John Fields wrote:
>> On Wed, 22 Dec 2004 13:56:07 GMT, vonroach <hadrainc@earthlink.net>

>>> Then comes the wild assertion
>>> that when a number is divided by nothing, it becomes infinite.
>>
>> ---
>> ???
>>
>> For
>>
>>              1
>>         x = ---
>>              n
>>
>> x grows without bound as n approaches zero, no?
>
>Exactly: graph y = 1 / x
>
>You get a graph that loos like this:
>(Both the  ---- line and the horizontal segments of ... are y = 0, drawn
>as such since to show what the graph line looks like without being
>overlapped by the origin (zero point) line.)
>
>
>y = 1 / x:
>
>                   | (doesn't quite reach 0,
>                   |.  <--  since y = undefiend for x = 0)
>                   |.
>                   | ..
>(<- etc) .......   |   ....... (etc ->)
>         -------..-+----------
>                  .|
>             -->  .|
>   (doesn't quite  |
>      reach 0, since y = undefiend for x = 0)
>

---
Unde_fiend_? I like that!-)

How about if we redraw the graph to look something like this:

y = 1 / x:

OXO
|
-

-
|.
| .
|   .
|      .
--.------0,0--------
.     |
.   |
. |
.|
-

-
|
OXO

with the discontinuities in plus and minus Y being used to allow us to
ignore the unimportant values (to us) of Y so that we can get to
infinity (ASCII OXO)?

That way we could (by sliding the discontinuity up and down) also plot
y = tan phi when phi was at, and also close to, 90�.

--
John Fields
```
 0
Reply John 12/22/2004 9:20:31 PM

```Nicholas O. Lindan wrote:
> "robert j. kolker" <nowhere@nowhere.net> wrote
>
>>> Then why can you not perform 1/0 ? (or n/0)
>>
>> If n/0 for n not 0 had a value then it would be equal to 0 and not
>> equal to 0 at the same time.
>
> ???
>
> The common contrarian take is:
>
> 1 / 0 = oo
> n / 0 = n * oo
> 0 / 0 = 0 * oo = 1
>
> I take the stance that 0 and oo are imaginary and sticky.  Once
> you have an equation with a 0 in it you are stuck with the zero.

Oh?

2^0 = 1

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/22/2004 9:32:35 PM

```robert j. kolker wrote:
> Alfred Z. Newmane wrote:
>
>>
>> Then why can you not perform 1/0 ? (or n/0)
>
> If n/0 for n not 0 had a value then it would be equal to 0 and not
> equal to 0 at the same time. Contradictions are not permitted.

I know, that was my silent point :-P (that ultimately, you cannot div by
zero.)

```
 0
Reply Alfred 12/22/2004 9:45:56 PM

```Nicholas O. Lindan wrote:
> "robert j. kolker" <nowhere@nowhere.net> wrote
>
>>> Then why can you not perform 1/0 ? (or n/0)
>>
>> If n/0 for n not 0 had a value then it would be equal to 0 and not
>> equal to 0 at the same time.
>
> ???
>
> The common contrarian take is:
>
> 1 / 0 = oo
> n / 0 = n * oo
> 0 / 0 = 0 * oo = 1

oo (infinity isn't a number) so you cannot use it this way.

```
 0
Reply Alfred 12/22/2004 9:47:36 PM

```Nicholas O. Lindan wrote:
> "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>
>> Sorry to nit pick, but in most any proper clac it should be written
>> as (-1)^(1/2), less you get -1 from -1^1/2, due to the '-' being
>> evaluated last. At least thats what happens in my TI86.
>
> That's the problem here.  Folks are using the wrong calculator.

Exactly.

> On an hp49 (physically a horrible peice of junk, now made by
> Casio(?), don't buy one) there is at least an 'oo' key.

Good grief... I thought all of those calculators were ordered destroyed
for fear of national security?

> It complains about oo when 1^0/ is _entered_, but it happily
> uses 10^500 when it comes time to numerically evaluate oo.

My TI simply gives 1e500

> Those for who Reversed not their Polish is 1^0/ is an
> asciigram for '1 [enter] 0 [divide]'

Ah, the old HP Reversed Polish notation :)

```
 0
Reply Alfred 12/22/2004 9:52:59 PM

```k wallace wrote:
> Kevin Aylward wrote:
>> vonroach wrote:
>>
>>> On Mon, 20 Dec 2004 14:34:03 -0000, BB <BB@BB.BB> wrote:
>>>
>>>
>>>> The divisor would have to be something smaller than 0 like -2.
>>>> Therefore zero is both even and negative.
>>>
>>> Whoa!  A new concept: -0.  Let's make up some other numbers. I
>>> suggest wizzad and fugawe. I'd have suggested Arunda, but I believe
>>> some obscure African group already uses that in their alphabet.
>>
>>
>> -0 often/usually signifies a limit approaching from the negative
>> direction.
>
> But that is an indication of direction to approach from, NOT a sign on
> the zero. When approaching f(x) from -0, we are not somehow computing
> with "negative zero".
> So while "-0" may have a defined meaning, it is certainly not
>   "negative zero".

Exactly. I was gonan pot the same thing jsut before I saw your post.

> This is getting too silly.

Well it seems a lot of debates I've seen on usenet become over inflated
by people who know nothing of what they are talking about, and the OP is
no wiser than before he made the initial post. Even with all the
knowledgeable posts abroad, they get lost in the mix of utter ignorance,
or so it seems.

It's really sad if you really think about it...

```
 0
Reply Alfred 12/22/2004 9:58:29 PM

```John Fields wrote:
> On Wed, 22 Dec 2004 10:30:37 -0800, "Alfred Z. Newmane"
> <a.newmane.remove@eastcoastcz.com> wrote:

[...]

>> y = 1 / x:
>>
>>                   | (doesn't quite reach 0,
>>                   |.  <--  since y = undefiend for x = 0)
>>                   |.
>>                   | ..
>> (<- etc) .......   |   ....... (etc ->)
>>         -------..-+----------
>>                  .|
>>             -->  .|
>>   (doesn't quite  |
>>      reach 0, since y = undefiend for x = 0)
>>
>
> ---
> Unde_fiend_? I like that!-)

Oops... nicks picks, nit picks... ;-P

> How about if we redraw the graph to look something like this:
>
>
> y = 1 / x:
>
>                   OXO
>                    |
>                    -
>
>                    -
>                    |.
>                    | .
>                    |   .
>                    |      .
>          --.------0,0--------
>              .     |
>                .   |
>                  . |
>                   .|
>                    -
>
>                    -
>                    |
>                   OXO
>
> with the discontinuities in plus and minus Y being used to allow us to
> ignore the unimportant values (to us) of Y so that we can get to
> infinity (ASCII OXO)?

I like your graph better than mine, well done.

> That way we could (by sliding the discontinuity up and down) also plot
> y = tan phi when phi was at, and also close to, 90�.

Good point :-)

```
 0
Reply Alfred 12/22/2004 10:00:30 PM

```"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
> Nicholas O. Lindan wrote:
> > 1 / 0 = oo
> > n / 0 = n * oo
> > 0 / 0 = 0 * oo = 1
>
> oo (infinity isn't a number) so you cannot use it this way.

Yes, that's my point.  Keep track of oo, don't merge it with
numbers.

j [sqrt(-1)] isn't a number but we still mix it up with numbers.
For infinity I can look in the sky.  For 0 I can examine my
bank balance.  But for j I can't look anywhere, but still
it has use.  With that perspective oo + 1 may be worth
manipulating.

I will admit, I find no use for 1/0 and 1 + oo > oo.
It's a mental itch.  And here's this scratching post.

As justification, j was pretty useless/undefined/don't
talk about it for till (someone famous) came up with e^jx,
which on the face of it makes even less sense.

So, as hobby, I am exploring the idea that if you can
keep track of oo and 1/0 and 4*0 it might have some

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 10:12:39 PM

```"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote

> Well it seems a lot of debates I've seen on usenet become over inflated
> by people who know nothing of what they are talking about, and the OP is
> no wiser than before he made the initial post. Even with all the
> knowledgeable posts abroad, they get lost in the mix of utter ignorance,
> or so it seems.  It's really sad if you really think about it...

"A tale, told by and idiot, full of sound and fury, signifying nothing."
Willy the Shake

For me, my choice is to endlessly converse about 1/0 or go back to
making cold sales calls.

Sort of like: "What will the dog eat before it consents to eating dog food."

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 10:19:59 PM

```John Fields wrote:
>                   OXO
>                    -
>                    |.
>                    | .
>                    |   .
>                    |      .
>          --.------0,0--------
>              .     |
>                .   |
>                  . |
>                   .|
>                    -
>
>                    -
>                    |
>                   OXO

One infinity, one zero.  +oo == -oo; +0 == -0.  Neither
actually exist and you can approach from the direction of

From the graph I would say 1/0 is oo.

Somebody wrote a whole book on '0', I have (had?) a copy
but darned if I can find it.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/22/2004 10:26:49 PM

```On Wed, 22 Dec 2004 22:26:49 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

>John Fields wrote:
>>                   OXO
>>                    -
>>                    |.
>>                    | .
>>                    |   .
>>                    |      .
>>          --.------0,0--------
>>              .     |
>>                .   |
>>                  . |
>>                   .|
>>                    -
>>
>>                    -
>>                    |
>>                   OXO
>
>
>One infinity, one zero.  +oo == -oo; +0 == -0.  Neither
>actually exist and you can approach from the direction of
>
>From the graph I would say 1/0 is oo.

---
Seems to make sense, doesn't it?
---

>Somebody wrote a whole book on '0', I have (had?) a copy
>but darned if I can find it.

---
I got a book on 'e', but every time I go looking for it it takes me
just as long to find it as it took the time before that, even if I
start looking for it where I left it. :^)

--
John Fields
```
 0
Reply John 12/22/2004 11:50:54 PM

```On Mon, 20 Dec 2004 15:36:15 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote, in part:

>"John Sefton" <john@petcom.com> wrote
>
>> 0 can't be divided by itself,
>
>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>
>It works if the only three numbers in the universe are
>0, 1, and infinity -- A number system that seems very
>suited to usenet.

It is possible to make a set of consistent rules for dividing by zero.

In general for ordinary multiplication and division, if a/b = c, then a
= b*c, and if a = b*c, then a/b = c.

We also know that 0 times any of the old-fashioned numbers we know about
makes 0.

So, if 5/0 = ?, then 5 = 0*?. ? cannot possibly be any number we know
about. Could ? possibly be positive infinity?

What about 0/0 = ?. 0 = 0 * ? is true if ? is any number, positive or
negative; ? can also be zero. Can we say that ? is any finite number?

It turns out those answers are not quite true.

0 = 0 * 0.

Also, 0 = -1 * 0.

So, if 5 = 0 * ?, it's also true that 5 = 0 * -1 * ?, and it's also true
that 5 = 0 * 0 * ?. So ? has to be either plus or minus infinity, or
infinity squared, or infinity cubed, and so on. And even that isn't
*quite* right, but it comes close.

If 5 = 0 * ?, then 0 * 0 * ? can be 0 * 5, or it can be 0 * ?, depending
on which two items you multiply by first.

This means that 0/0 has to be allowed to be plus or minus infinity as
well as any finite number, including zero.

Because the rules break down so badly for dividing by zero, including
the fact that multiplication now stops being associative, mathematicians
have chosen to concentrate on studying only the "real numbers", which
are all finite quantities. This way, they can deduce new theorems from
the properties that multiplication and division have on those numbers;
generalizing to division by zero is not normally done because it appears
that it would just create awkward exceptions in every mathematical
proof, without being fruitful, without producing new, useful results.

John Savard
http://home.ecn.ab.ca/~jsavard/index.html
```
 0
Reply jsavard 12/23/2004 5:48:17 AM

```On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote, in part:

>Slightly OT, is there an accepted ASCII-gram for square root?

Here's an example of how I draw equations in ASCII art.

_
/  theta         /  psi     pi \         /  psi     pi \
|            sin |  ----- + ---  | + cos |  ----- + ---  |
|                 \   2      4  /         \   2      4  /
|          ------------------------------------------------- , d psi
|                       ____________________________
|                      /        2  /  psi     pi \
|                     /  1 + tan  |  ----- - ---  |
_/  0                 \/             \   2      4  /

John Savard
http://home.ecn.ab.ca/~jsavard/index.html
```
 0
Reply jsavard 12/23/2004 5:50:07 AM

```On Thu, 23 Dec 2004 05:48:17 GMT, jsavard@excxn.aNOSPAMb.cdn.invalid
(John Savard) wrote:

>Because the rules break down so badly for dividing by zero, including
>the fact that multiplication now stops being associative, mathematicians
>have chosen to concentrate on studying only the "real numbers", which
>are all finite quantities. This way, they can deduce new theorems from
>the properties that multiplication and division have on those numbers;
>generalizing to division by zero is not normally done because it appears
>that it would just create awkward exceptions in every mathematical
>proof, without being fruitful, without producing new, useful results.
>

Except that in electronic design, especially in realtime embedded
systems, the issues can't be avoided. If you digitize zero volts, and
that's the denominator in some process equation, you can't just say
"oh well, that's not defined/fruitful". Doubly so in a deep embedded
system where you have no audience to complain to.

John

```
 0
Reply John 12/23/2004 6:04:25 AM

```John Larkin wrote:
> On Thu, 23 Dec 2004 05:48:17 GMT, jsavard@excxn.aNOSPAMb.cdn.invalid
> (John Savard) wrote:
>
>
>
>>Because the rules break down so badly for dividing by zero, including
>>the fact that multiplication now stops being associative, mathematicians
>>have chosen to concentrate on studying only the "real numbers", which
>>are all finite quantities. This way, they can deduce new theorems from
>>the properties that multiplication and division have on those numbers;
>>generalizing to division by zero is not normally done because it appears
>>that it would just create awkward exceptions in every mathematical
>>proof, without being fruitful, without producing new, useful results.
>>
>
>
> Except that in electronic design, especially in realtime embedded
> systems, the issues can't be avoided. If you digitize zero volts, and
> that's the denominator in some process equation, you can't just say
> "oh well, that's not defined/fruitful". Doubly so in a deep embedded
> system where you have no audience to complain to.
>
> John
>

I have found, however, that if one has a model that leads one to a
divide by zero problem one is suffering from one of two problems:  one,
an insufficient model, or two, an inaccurate measurement (which one can
sophomoricaly lump into one, if one is so inclined).

It is always necessary to ask yourself "why am I allowing a division by
something that may go to zero?"  "What does it mean if my 'x' is zero
here?", etc., and code accordingly.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
```
 0
Reply Tim 12/23/2004 6:33:23 AM

```I read in sci.electronics.design that John Savard <jsavard@excxn.aNOSPAM
b.cdn.invalid> wrote (in <41ca5c5c.1513665@news.ecn.ab.ca>) about 'Is
zero even or odd?', on Thu, 23 Dec 2004:
>On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
>wrote, in part:
>
>>Slightly OT, is there an accepted ASCII-gram for square root?
>
>Here's an example of how I draw equations in ASCII art.
>
>    _
>   /  theta         /  psi     pi \         /  psi     pi \
>  |            sin |  ----- + ---  | + cos |  ----- + ---  |
>  |                 \   2      4  /         \   2      4  /
>  |          ------------------------------------------------- , d psi
>  |                       ____________________________
>  |                      /        2  /  psi     pi \
>  |                     /  1 + tan  |  ----- - ---  |
>_/  0                 \/             \   2      4  /
>

You obviously belong to the 'mural' school of ASCII art, like Fred
Bloggs.

--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/23/2004 7:03:52 AM

```Nicholas O. Lindan wrote:
> "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>> Nicholas O. Lindan wrote:
>>> 1 / 0 = oo
>>> n / 0 = n * oo
>>> 0 / 0 = 0 * oo = 1
>>
>> oo (infinity isn't a number) so you cannot use it this way.
>
> Yes, that's my point.  Keep track of oo, don't merge it with
> numbers.
>
> j [sqrt(-1)] isn't a number but we still mix it up with numbers.

Of course it is a number, thats why we treat it as such.

> For infinity I can look in the sky.  For 0 I can examine my
> bank balance.  But for j I can't look anywhere,

Not really relevant. Numbers only "exist" in the mind.

>but still
> it has use.  With that perspective oo + 1 may be worth
> manipulating.
>
> I will admit, I find no use for 1/0 and 1 + oo > oo.
> It's a mental itch.  And here's this scratching post.
>
> As justification, j was pretty useless/undefined/don't

What do you mean by this?

Most things have no meaning if we don't know what it is.

> talk about it for till (someone famous) came up with e^jx,
> which on the face of it makes even less sense.

Not to a mathematician.

>
> So, as hobby, I am exploring the idea that if you can
> keep track of oo and 1/0 and 4*0 it might have some

"Keeping track" of oo is already well established in mathematics. You
seem to be implying that this idea is novel.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/23/2004 7:46:47 AM

```
Kevin Aylward schrieb:
> Nicholas O. Lindan wrote:
> > j [sqrt(-1)] isn't a number but we still mix it up with numbers.
>
> Of course it is a number, thats why we treat it as such.
>
> > For infinity I can look in the sky.  For 0 I can examine my
> > bank balance.  But for j I can't look anywhere,
>
> Not really relevant. Numbers only "exist" in the mind.

Points on a plane are often modelled as complex numbers, so you need
only look as far as graph paper to "see" them.

Bring more popcorn!
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/23/2004 9:50:30 AM

```In article <LSjyd.9199\$yK.1676@newsread3.news.atl.earthlink.net>,
"Nicholas O. Lindan" <see@sig.com> wrote:
>"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>
>> Am I missing something here?

>No, not really - nobody has said anything profound yet.

You are kidding.  Didn't you think the stuff that Mati Meron
wrote was profound?  What he talked about is one of the
building blocks of making a mathematics.  Did you miss the
difference between non-existence and undefined?

<snip>

/BAH

Subtract a hundred and four for e-mail.
```
 0
Reply jmfbahciv 12/23/2004 11:29:32 AM

```Michael Mendelsohn wrote:
> Kevin Aylward schrieb:
>> Nicholas O. Lindan wrote:
>>> j [sqrt(-1)] isn't a number but we still mix it up with numbers.
>>
>> Of course it is a number, thats why we treat it as such.
>>
>>> For infinity I can look in the sky.  For 0 I can examine my
>>> bank balance.  But for j I can't look anywhere,
>>
>> Not really relevant. Numbers only "exist" in the mind.
>

Ahmm...

> Points on a plane are often modelled as complex numbers, so you need
> only look as far as graph paper to "see" them.

Numbers are concepts. Graph paper drawings are only representaions of
numbers, not numbers themselves.

How would you go about representing a complex vector "space number"? Now
we need 9 dimensions for our graph paper.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/23/2004 12:47:50 PM

```Alfred Z. Newmane wrote:

> Nicholas O. Lindan wrote:
>
>>"robert j. kolker" <nowhere@nowhere.net> wrote
>>
>>
>>>>Then why can you not perform 1/0 ? (or n/0)
>>>
>>>If n/0 for n not 0 had a value then it would be equal to 0 and not
>>>equal to 0 at the same time.
>>
>>???
>>
>>The common contrarian take is:
>>
>>1 / 0 = oo
>>n / 0 = n * oo
>>0 / 0 = 0 * oo = 1
>
>
> oo (infinity isn't a number) so you cannot use it this way.
>
>

Well, if you move out of pure math into something more applied,
like physics or signal processing, you find a nice little thing
called the Dirac delta function.  This seems to have confounded
mathemeticians for a while before they finally came around and
decided that it really does work.

This wonderful function has infinite height and zero width, yet
it has area 1.  Granted, you can work with a limit as the width
goes to 0, but you don't have to.

Think Fourier series and Fourier analysis.  These wouldn't work
without the Dirac delta function.

A wonderful example of 0 * oo = 1.

Another is renormalization theory in QED (Quantum Electrodynamics).
There are several infinities in the theory that appeared to make
the results nonsense.  However, if you keep track very carefully,
you can get the infinities to cancel and come up with predictions
that match measurements very accurately.

This is an example of (oo + n) - oo = n as well as oo/oo = 1.

So all the statements about how these combinations of 0 and oo are
undefined are only part of the story.  Sometimes they do make sense.

This has been a very entertaining topic.  I'll hate to eventually see
it die...  8-)

```
 0
Reply Gordon 12/23/2004 2:03:01 PM

```Gordon Weast wrote:

>
> Another is renormalization theory in QED (Quantum Electrodynamics).
> There are several infinities in the theory that appeared to make
> the results nonsense.  However, if you keep track very carefully,
> you can get the infinities to cancel and come up with predictions
> that match measurements very accurately.

And physicists think it an ugly bodge. Clearly the infinities are failures of
the theory, but the failures cancel out.

--
Dirk

The Consensus:-
The political party for the new millenium
http://www.theconsensus.org
```
 0
Reply Dirk 12/23/2004 3:38:12 PM

```Gordon Weast wrote:
> Alfred Z. Newmane wrote:
>
>> Nicholas O. Lindan wrote:
>>
>>> "robert j. kolker" <nowhere@nowhere.net> wrote
>>>
>>>
>>>>> Then why can you not perform 1/0 ? (or n/0)
>>>>
>>>> If n/0 for n not 0 had a value then it would be equal to 0 and not
>>>> equal to 0 at the same time.
>>>
>>> ???
>>>
>>> The common contrarian take is:
>>>
>>> 1 / 0 = oo
>>> n / 0 = n * oo
>>> 0 / 0 = 0 * oo = 1
>>
>>
>> oo (infinity isn't a number) so you cannot use it this way.
>>
>>
>
> Well, if you move out of pure math into something more applied,
> like physics or signal processing, you find a nice little thing
> called the Dirac delta function.  This seems to have confounded
> mathemeticians for a while before they finally came around and
> decided that it really does work.
>
> This wonderful function has infinite height and zero width, yet
> it has area 1.

Not really technically accurate. The Dirac function is defined by
limits, not by "infinite height" and "zero width"

>Granted, you can work with a limit as the width
> goes to 0, but you don't have to.

Yes you do.

>
> Think Fourier series and Fourier analysis.  These wouldn't work
> without the Dirac delta function.

This is not really true. Sure, *one* method of proving the Fourier
transform pair is to use the Dirac function, but this approach is not
required, most treatments actually use a more direct approach, e.g.
integral sin(Lx)/x as L->oo.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/23/2004 3:55:00 PM

```"John Savard" <jsavard@excxn.aNOSPAMb.cdn.invalid> wrote

> So, if 5/0 = ?, then 5 = 0*?. Could ? possibly be positive infinity?

5 / 0 = ?
5 * 1/0 = ?
5 * oo = ?

So ? is equal to 5 infinities added together.

oo, like 0 is neither positive or negative.  It can be approached
from + or -.  Think of the number line as a circle, or pointing to
the big bang in the night sky.

> What about 0/0 = ?. 0 = 0 * ? is true if ? is any number, positive or
> negative; ? can also be zero. Can we say that ? is any finite number?

Try 1.  Works pretty well in my book.

> Also, 0 = -1 * 0.

& oo = -1 * oo

> So, if 5 = 0 * ?, it's also true that 5 = 0 * -1 * ?

"?" isn't a good substitute for and unknown.  Statements look like
queries.  I'm substituting "x"

> that 5 = 0 * 0 * x.

We part company:

0 * 0 = 0^2

As in

oo * oo = oo^2 = "Aleph 1" in Cantor's book.  It is the first oo (Aleph 1)
that can be proven to be larger than ordinary oo (Aleph 0).

Cantor's notation, if extended, would make 0 into "Omega 0", 0^2 "Omega 1".
I think we have the alphas and omegas confused.  Or, what the heck:
0 is the end of it all.  oo the beginning.

> infinity squared, or infinity cubed, and so on.
> And even that isn't *quite* right, but it comes close.

Look up Cantor.

> If 5 = 0 * ?, then 0 * 0 * ? can be 0 * 5, or it can be 0 * ?, depending
> on which two items you multiply by first.

Ah:

0 * 5 = 0 * 0 * x

= (0 * 0) * x
= 0^2 * x
5 = 0 * x

0 * 5 = 0 * (0 * x)
5 = (0 * x)
5 = 0 * x

If you allow that 0 * 0 == 0^2 the quandary resolves itself.

> This means that 0/0 has to be allowed to be plus or minus infinity as
> well as any finite number, including zero.

In my scheme 0/0 == 1

> Because the rules break down so badly for dividing by zero,

The answer may be new rules. And why not, the alternative is being
stuck in 7th grade in Jr. High School.

> the "real numbers", which are all finite quantities.

But the size of the set of real numbers is Aleph 1 (oo^2).  The
integers and reals have values that run to Aleph 0.  Finite I
don't think is the word here.

> division by zero is not normally done because it appears
> that it would [not be] fruitful, or produce new, useful results.

I have to agree.  I don't find any use for 0^2 myself.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 4:18:15 PM

```"John Larkin" <john@spamless.usa> wrote

> Except that in electronic design, especially in realtime embedded
> systems, the issues can't be avoided. If you digitize zero volts, and
> that's the denominator in some process equation, you can't just say
> "oh well, that's not defined/fruitful". Doubly so in a deep embedded
> system where you have no audience to complain to.

Too true.

The response to x/0 is to set the output to it's fail safe value or
freeze it, and optionally sound the alarm and declare the input 'failed'.

0/0 pops up now and then: The system does the right thing if
this is treated as 1.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 4:24:30 PM

```"Tim Wescott" <tim@wescottnospamdesign.com> wrote

> It is always necessary to ask yourself "why am I allowing a division by
> something that may go to zero?"  "What does it mean if my 'x' is zero
> here?", etc., and code accordingly.

Yup.  The response is process dependant.  Gee, does that mean x/0 must
be what you _need_ it to be? (-it's a joke-).

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 4:27:26 PM

```Kevin Aylward schrieb:

> Not really relevant. Numbers only "exist" in the mind.

Great, now we define what is a number.  Bertrand Russel threw
up his hands and whats-his-name declared he can prove it can't
be done.

Numbers, as are what are not just in the head, are 1:1 mappings
to things.

1 apple, 2 apples ... but sqrt(-1)apples, why that's only

> Points on a plane are often modeled as complex numbers, so you need
> only look as far as graph paper to "see" them.

"Modeled" is the operative word.  I see only graph paper,
the rest is imagination = dreams = not really there.

sqrt(-1) is used in calculations to indicate orthogonality,
where never the twain shall meet and the values do not mix
indiscriminately.  And never is heard a discouraging word  ...
Oklahoma isn't on Usenet, I take it.

Can we settle on "sqrt (-1) is a different kind of number"?

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 4:40:31 PM

```"Gordon Weast" <gweast@mathworks.com> wrote

> Well, if you move out of pure math into something more applied,
> like physics or signal processing, you find a nice little thing
> called the Dirac delta function.  This seems to have confounded
> mathematicians for a while before they finally came around and
> decided that it really does work.
>
> This wonderful function has infinite height and zero width, yet
> it has area 1.  Granted, you can work with a limit as the width
> goes to 0, but you don't have to.
>
> Think Fourier series and Fourier analysis.  These wouldn't work
> without the Dirac delta function.
>
> A wonderful example of 0 * oo = 1.

Words out of my mouth.  Saves me a lot of typing.

> Another is renormalization theory in QED (Quantum Electrodynamics).
> There are several infinities in the theory that appeared to make
> the results nonsense.  However, if you keep track very carefully,
> you can get the infinities to cancel and come up with predictions
> that match measurements very accurately.
> This is an example of (oo + n) - oo = n as well as oo/oo = 1.
>
> So all the statements about how these combinations of 0 and oo are
> undefined are only part of the story.  Sometimes they do make sense.

OK, so no I am left wordless ... Ha!

> This has been a very entertaining topic.  I'll hate to eventually see
> it die...  8-)

Oh, it will go on forever, stuck on a roundabout in information
high street.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 4:47:21 PM

```Nicholas O. Lindan wrote:
> But the size of the set of real numbers is Aleph 1 (oo^2).

Aleph-1 is at least aleph-null^aleph-null.
--
John W. Kennedy
"The pathetic hope that the White House will turn a Caligula into a
Marcus Aurelius is as na�ve as the fear that ultimate power inevitably
corrupts."
-- James D. Barber (1930-2004).
```
 0
Reply John 12/23/2004 5:22:02 PM

```"John W. Kennedy" <jwkenne@attglobal.net> writes:

> Aleph-1 is at least aleph-null^aleph-null.

On what do you base this assertion?

```
 0
Reply Torkel 12/23/2004 5:23:00 PM

```On Thu, 23 Dec 2004 12:22:02 -0500, John W. Kennedy wrote:
> Nicholas O. Lindan wrote:
>> But the size of the set of real numbers is Aleph 1 (oo^2).

> Aleph-1 is at least aleph-null^aleph-null.

No, it's the other way around.  Since aleph_1 is by definition the
smallest uncountable cardinal, and since the reals are uncountable, it
follows that c (= 2^aleph_0 = aleph_0^aleph_0), the cardinality of the
continuum, cannot be less than aleph_1.  On the other hand, it could be
that c is quite huge among the alephs.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
```
 0
Reply Dave 12/23/2004 6:10:11 PM

```Kevin Aylward schrieb:
> Michael Mendelsohn wrote:
> > Points on a plane are often modelled as complex numbers, so you need
> > only look as far as graph paper to "see" them.
>
> Numbers are concepts. Graph paper drawings are only representaions of
> numbers, not numbers themselves.
>
> How would you go about representing a complex vector "space number"? Now
> we need 9 dimensions for our graph paper.

Have you never heard of origami?

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/23/2004 6:15:33 PM

```"Nicholas O. Lindan" schrieb:
> 0/0 pops up now and then: The system does the right thing if
> this is treated as 1.

If in measuring a resistor, we find 0.0A at 0.0V, is the resistance 1
Ohm, then?

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/23/2004 6:18:24 PM

```Tim Wescott wrote:

> John Larkin wrote:
>
>> On Thu, 23 Dec 2004 05:48:17 GMT, jsavard@excxn.aNOSPAMb.cdn.invalid
>> (John Savard) wrote:
>>
>>
>>
>>> Because the rules break down so badly for dividing by zero, including
>>> the fact that multiplication now stops being associative, mathematicians
>>> have chosen to concentrate on studying only the "real numbers", which
>>> are all finite quantities. This way, they can deduce new theorems from
>>> the properties that multiplication and division have on those numbers;
>>> generalizing to division by zero is not normally done because it appears
>>> that it would just create awkward exceptions in every mathematical
>>> proof, without being fruitful, without producing new, useful results.
>>>
>>
>>
>> Except that in electronic design, especially in realtime embedded
>> systems, the issues can't be avoided. If you digitize zero volts, and
>> that's the denominator in some process equation, you can't just say
>> "oh well, that's not defined/fruitful". Doubly so in a deep embedded
>> system where you have no audience to complain to.
>>
>> John
>>
>
> I have found, however, that if one has a model that leads one to a
> divide by zero problem one is suffering from one of two problems:  one,
> an insufficient model, or two, an inaccurate measurement (which one can
> sophomoricaly lump into one, if one is so inclined).
>
> It is always necessary to ask yourself "why am I allowing a division by
> something that may go to zero?"  "What does it mean if my 'x' is zero
> here?", etc., and code accordingly.
>
if your dealing with microprocessor code a simple Bit test of bit 0
(first bit) will tell you if the value is Odd/even..
if its on its Odd value otherwise its Even. and that covers the
zero problem.

```
 0
Reply Jamie 12/23/2004 6:55:51 PM

```Dirk Bruere at Neopax wrote:
> Gordon Weast wrote:
>
>>
>> Another is renormalization theory in QED (Quantum Electrodynamics).
>> There are several infinities in the theory that appeared to make
>> the results nonsense.  However, if you keep track very carefully,
>> you can get the infinities to cancel and come up with predictions
>> that match measurements very accurately.
>
> And physicists think it an ugly bodge.

Actually, I think the physicists think its just a bit annoying, its the
mathematicians that think its the ugly bodge.

>Clearly the infinities are
> failures of the theory,

Or a failure of the mathematics.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/23/2004 7:02:20 PM

```Nicholas O. Lindan wrote:
> Kevin Aylward schrieb:
>
>> Not really relevant. Numbers only "exist" in the mind.
>
> Great, now we define what is a number.  Bertrand Russel threw
> up his hands and whats-his-name declared he can prove it can't
> be done.
>
> Numbers, as are what are not just in the head, are 1:1 mappings
> to things.
>
> 1 apple, 2 apples ... but sqrt(-1)apples, why that's only
> in your imagination.
>
>> Points on a plane are often modeled as complex numbers, so you need
>> only look as far as graph paper to "see" them.
>
> "Modeled" is the operative word.  I see only graph paper,
> the rest is imagination = dreams = not really there.
>
> sqrt(-1) is used in calculations to indicate orthogonality,

It can do, but that is not the only reason for sqrt(-1). Its certainly
not how it came about in the first place.

> where never the twain shall meet and the values do not mix
> indiscriminately.  And never is heard a discouraging word  ...
> Oklahoma isn't on Usenet, I take it.
>
> Can we settle on "sqrt (-1) is a different kind of number"?

No.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/23/2004 7:02:27 PM

```"John W. Kennedy" <jwkenne@attglobal.net> wrote

> > But the size of the set of real numbers is Aleph 1 (oo^2).
> Aleph-1 is at least aleph-null^aleph-null.

Quite right, slip of the fingers (probably the mind, but I
always blame it on the fingers).

Should read ... Aleph 1 (oo^oo) ...

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 7:46:06 PM

```"Dave Seaman" <dseaman@no.such.host> wrote
> On Thu, 23 Dec 2004 12:22:02 -0500, John W. Kennedy wrote:
> > Aleph-1 is at least aleph-null^aleph-null.
>
> No, it's the other way around.  Since aleph_1 is by definition the
> smallest uncountable cardinal, and since the reals are uncountable, it
> follows that c (= 2^aleph_0 = aleph_0^aleph_0), the cardinality of the
> continuum, cannot be less than aleph_1.  On the other hand, it could be
> that c is quite huge among the alephs.

I'm lost.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 7:48:08 PM

```Kevin Aylward wrote:

> Dirk Bruere at Neopax wrote:
>
>>Gordon Weast wrote:
>>
>>
>>>Another is renormalization theory in QED (Quantum Electrodynamics).
>>>There are several infinities in the theory that appeared to make
>>>the results nonsense.  However, if you keep track very carefully,
>>>you can get the infinities to cancel and come up with predictions
>>>that match measurements very accurately.
>>
>>And physicists think it an ugly bodge.
>
>
> Actually, I think the physicists think its just a bit annoying, its the
> mathematicians that think its the ugly bodge.
>
>
>>Clearly the infinities are
>>failures of the theory,
>
>
> Or a failure of the mathematics.

Is there a difference?

--
Dirk

The Consensus:-
The political party for the new millenium
http://www.theconsensus.org
```
 0
Reply Dirk 12/23/2004 7:54:20 PM

```"Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote

> If in measuring a resistor, we find 0.0A at 0.0V, is the resistance 1
> Ohm, then?

Touche.

But, yes, I'll say it is 1, just not in conventional ohms.
At 0.0A and 0.0V any scaling factor can apply to the volts
and amps without changing the measurement:

1 new volt / 1 new amp = new value of the resistor.

0 new volts / 0 new amps = 1 * (1 volt / 1 amp) = new value of the resistor.

Value of the resistor = 1 new ohm.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 7:56:18 PM

```"Jamie" <jamie_5_not_valid_after_5_Please@charter.net> wrote

> if your dealing with microprocessor code a simple Bit test of bit 0
> (first bit) will tell you if the value is Odd/even..
> if its on its Odd value otherwise its Even. and that covers the
> zero problem.

Once more, a PIC saves the day!

Cheers from the crowds ...

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/23/2004 7:58:42 PM

```I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
'Is zero even or odd?', on Thu, 23 Dec 2004:
>"Dave Seaman" <dseaman@no.such.host> wrote
>> On Thu, 23 Dec 2004 12:22:02 -0500, John W. Kennedy wrote:
>> > Aleph-1 is at least aleph-null^aleph-null.
>>
>> No, it's the other way around.  Since aleph_1 is by definition the
>> smallest uncountable cardinal, and since the reals are uncountable, it
>> follows that c (= 2^aleph_0 = aleph_0^aleph_0), the cardinality of the
>> continuum, cannot be less than aleph_1.  On the other hand, it could be
>> that c is quite huge among the alephs.
>
>I'm lost.

You need to study the math of infinities. Aleph-null is the smallest
infinity, and whatever you do to it with finite numbers doesn't change
it. Many operations with itself, even, don't change it. But raising it
to its power, {-}o^({-}o), creates a new infinity with different
properties. Although it's called aleph-one, no-one knows whether it is
the *next* infinity after aleph-null, or whether there are other
infinities in between.

No, I can't say I *understand* it either. The above was written in
parrot mode.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/23/2004 8:18:14 PM

```Nicholas O. Lindan wrote:
> John Fields wrote:
>
>>                  OXO
>>                   -
>>                   |.
>>                   | .
>>                   |   .
>>                   |      .
>>         --.------0,0--------
>>             .     |
>>               .   |
>>                 . |
>>                  .|
>>                   -
>>
>>                   -
>>                   |
>>                  OXO
>
>
>
> One infinity, one zero.  +oo == -oo; +0 == -0.  Neither
> actually exist and you can approach from the direction of

lol- pre-coffee, I read this to say "neither of you actually exist..."
one of the better refutations I've seen on Usenet, I was thinking, and
Ok, continue on..
-kwallace

>
> From the graph I would say 1/0 is oo.
>
> Somebody wrote a whole book on '0', I have (had?) a copy
> but darned if I can find it.
>
```
 0
Reply k 12/23/2004 8:38:10 PM

```"Nicholas O. Lindan" schrieb:
> "Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote
> > If in measuring a resistor, we find 0.0A at 0.0V, is the resistance 1
> > Ohm, then?
>
> Touche.
>
> But, yes, I'll say it is 1, just not in conventional ohms.
> At 0.0A and 0.0V any scaling factor can apply to the volts
> and amps without changing the measurement:
>
> 1 new volt / 1 new amp = new value of the resistor.
>
> 0 new volts / 0 new amps = 1 * (1 volt / 1 amp) = new value of the resistor.
>
> Value of the resistor = 1 new ohm.

When checking it turned out that some thief had actually stolen the
resistor where 0V,0A was measured. The circuit was broken, but noone
noticed because the voltage was zero.

Hence, vacuum/an insulator/air has a resistance of 1 new Ohm?

Cheers
Michael

--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/23/2004 9:45:26 PM

```John Woodgate wrote:
>
> I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
> 'Is zero even or odd?', on Thu, 23 Dec 2004:
> >"Dave Seaman" <dseaman@no.such.host> wrote
> >> On Thu, 23 Dec 2004 12:22:02 -0500, John W. Kennedy wrote:
> >> > Aleph-1 is at least aleph-null^aleph-null.
> >>
> >> No, it's the other way around.  Since aleph_1 is by definition the
> >> smallest uncountable cardinal, and since the reals are uncountable, it
> >> follows that c (= 2^aleph_0 = aleph_0^aleph_0), the cardinality of the
> >> continuum, cannot be less than aleph_1.  On the other hand, it could be
> >> that c is quite huge among the alephs.
> >
> >I'm lost.
>
> You need to study the math of infinities. Aleph-null is the smallest
> infinity, and whatever you do to it with finite numbers doesn't change
> it. Many operations with itself, even, don't change it. But raising it
> to its power, {-}o^({-}o), creates a new infinity with different
> properties. Although it's called aleph-one, no-one knows whether it is
> the *next* infinity after aleph-null, or whether there are other
> infinities in between.

Whether (aleph_0)^{aleph_0} = aleph_1 or not isn't decided in the usual
set theories.

aleph_1 is the next infinity after aleph_0 (given the axiom of choice),
the question is, is 2^{aleph_0} the next infinity after aleph_0?  (And
generally, is 2^{aleph_{alpha}} the next infinity after aleph_{alpha}?)
```
 0
Reply George 12/23/2004 10:00:35 PM

```On Thu, 23 Dec 2004 20:18:14 +0000, John Woodgate wrote:
> I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
> 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>"Dave Seaman" <dseaman@no.such.host> wrote
>>> On Thu, 23 Dec 2004 12:22:02 -0500, John W. Kennedy wrote:
>>> > Aleph-1 is at least aleph-null^aleph-null.
>>>
>>> No, it's the other way around.  Since aleph_1 is by definition the
>>> smallest uncountable cardinal, and since the reals are uncountable, it
>>> follows that c (= 2^aleph_0 = aleph_0^aleph_0), the cardinality of the
>>> continuum, cannot be less than aleph_1.  On the other hand, it could be
>>> that c is quite huge among the alephs.
>>
>>I'm lost.

> You need to study the math of infinities. Aleph-null is the smallest
> infinity, and whatever you do to it with finite numbers doesn't change
> it. Many operations with itself, even, don't change it. But raising it
> to its power, {-}o^({-}o), creates a new infinity with different
> properties. Although it's called aleph-one, no-one knows whether it is
> the *next* infinity after aleph-null, or whether there are other
> infinities in between.

> No, I can't say I *understand* it either. The above was written in
> parrot mode.

It's a widespread belief (and one that is unfortunately perpetuated by some
popular expositions) that the cardinality of the reals is aleph_1.  Not so.
The cardinality of the reals is 2^aleph_0, which is the same as
aleph_0^aleph_0.  This cardinal is called c, for the cardinality of the
continuum.  The proposition that c = aleph_1 is called the continuum
hypothesis, and it is known to be independent of the usual axioms of set
theory.

<http://mathworld.wolfram.com/ContinuumHypothesis.html>

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
```
 0
Reply Dave 12/24/2004 12:35:20 AM

```On Thu, 23 Dec 2004 19:02:20 GMT, Kevin Aylward wrote:
> Dirk Bruere at Neopax wrote:
>> Gordon Weast wrote:

>>> Another is renormalization theory in QED (Quantum Electrodynamics).
>>> There are several infinities in the theory that appeared to make
>>> the results nonsense.  However, if you keep track very carefully,
>>> you can get the infinities to cancel and come up with predictions
>>> that match measurements very accurately.

>> And physicists think it an ugly bodge.

> Actually, I think the physicists think its just a bit annoying, its the
> mathematicians that think its the ugly bodge.

No, not at all.  It's not a function in the ordinary sense, but a
generalized function.  It's a linear functional defined on a certain
function space.

<http://mathworld.wolfram.com/DeltaFunction.html>.

>>Clearly the infinities are
>> failures of the theory,

> Or a failure of the mathematics.

Definitely not.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
```
 0
Reply Dave 12/24/2004 12:47:51 AM

```
Dave Seaman wrote:

>
> No, not at all.  It's not a function in the ordinary sense, but a
> generalized function.  It's a linear functional defined on a certain
> function space.

Here is an analogy. A function is like a vector. A delta "function" is
like a one form.

Bob Kolker

```
 0
Reply robert 12/24/2004 1:47:28 AM

```In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
John Woodgate  <noone@yuk.yuk> wrote:
>I read in sci.electronics.design that Matthew Russotto
><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>But sin (pi*x)/pi*x is
>>discontinous at zero.
>
>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>If not, it's 'squeezed'.

I'm not sure what you mean by 'squeezed'; it's piecewise continuous.

```
 0
Reply russotto 12/24/2004 4:53:44 AM

```I read in sci.electronics.design that Matthew Russotto
<russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>John Woodgate  <noone@yuk.yuk> wrote:
>>I read in sci.electronics.design that Matthew Russotto
>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>But sin (pi*x)/pi*x is
>>>discontinous at zero.
>>
>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>If not, it's 'squeezed'.
>
>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>
Squeezed: if the limits are equal, the value of the function at the
limit point cannot differ from the limit value.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/24/2004 5:57:43 AM

```"Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote

> When checking it turned out that some thief had actually stolen the
> resistor where 0V,0A was measured. The circuit was broken, but noone
> noticed because the voltage was zero.

The circuit wasn't connected.  Therefore no measurement was being
made.  V = IR has no relevance. R < oo to close the circuit and
for the equation to apply.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/24/2004 7:20:53 AM

```Dave Seaman wrote:
> On Thu, 23 Dec 2004 19:02:20 GMT, Kevin Aylward wrote:
>> Dirk Bruere at Neopax wrote:
>>> Gordon Weast wrote:
>
>
>>>> Another is renormalization theory in QED (Quantum Electrodynamics).
>>>> There are several infinities in the theory that appeared to make
>>>> the results nonsense.  However, if you keep track very carefully,
>>>> you can get the infinities to cancel and come up with predictions
>>>> that match measurements very accurately.
>
>>> And physicists think it an ugly bodge.
>
>> Actually, I think the physicists think its just a bit annoying, its
>> the mathematicians that think its the ugly bodge.
>
> No, not at all.

Nope.

>It's not a function in the ordinary sense, but a
> generalized function.

Ho hum. What isn't a function? We are discussing QED.

Go back up and read what was wrote. It started with "Another is
renormalization theory in QED..." Note the lack of mention of "Dirac
function"

>It's a linear functional defined on a certain
> function space.

What is? QED?

>
> <http://mathworld.wolfram.com/DeltaFunction.html>.

Oh... you mean the Dirac function. Well I know all about this, but you
are off on a tangent.

My "not at all" is regarding the infinities in QED. The Dirac function
was not part of the discussion at this point.

>
>>> Clearly the infinities are
>>> failures of the theory,
>
>> Or a failure of the mathematics.
>
> Definitely not.

Definitely is. The infinities in QED are unresolved.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

```
 0
Reply Kevin 12/24/2004 8:06:07 AM

```Referencing:
> <http://mathworld.wolfram.com/ContinuumHypothesis.html>

"Dave Seaman" <dseaman@no.such.host> wrote

> It's a widespread belief (and one that is unfortunately perpetuated by some
> popular expositions) that the cardinality of the reals is aleph_1.  Not so.
> The cardinality of the reals is 2^aleph_0, which is the same as
> aleph_0^aleph_0.  This cardinal is called c, for the cardinality of the
> continuum.  The proposition that c = aleph_1 is called the continuum
> hypothesis, and it is known to be independent of the usual axioms of set
> theory.

The latter part of the paragraph seems to support the view that
c = continuum = cardinality of the reals = aleph-0 ^ aleph-0 = aleph^1
which you claim in the first two sentences to be false.

Dazed and confused again.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/24/2004 8:21:39 AM

```I read in sci.electronics.design that Kevin Aylward
<salesEXTRACT@anasoft.co.uk> wrote (in <P5Qyd.43454\$ef5.2988@fe1.news.bl
ueyonder.co.uk>) about 'Is zero even or odd?', on Fri, 24 Dec 2004:

>Oh... you mean the Dirac function. Well I know all about this, but you
>are off on a tangent.

Does it have a tangent? If so, it is very small and lives inside
capacitors. You can see in the specs, tan[delta] = 0.001, for example.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/24/2004 8:55:14 AM

```Nicholas O. Lindan a �crit :
> Referencing:
>
>><http://mathworld.wolfram.com/ContinuumHypothesis.html>
>
>
> "Dave Seaman" <dseaman@no.such.host> wrote
>
>
>>It's a widespread belief (and one that is unfortunately perpetuated by some
>>popular expositions) that the cardinality of the reals is aleph_1.  Not so.
>>The cardinality of the reals is 2^aleph_0, which is the same as
>>aleph_0^aleph_0.  This cardinal is called c, for the cardinality of the
>>continuum.  The proposition that c = aleph_1 is called the continuum
>>hypothesis, and it is known to be independent of the usual axioms of set
>>theory.
>
>
> The latter part of the paragraph seems to support the view that
> c = continuum = cardinality of the reals = aleph-0 ^ aleph-0 = aleph^1
> which you claim in the first two sentences to be false.
>
> Dazed and confused again.

Reading trouble? The last part says explcitely that the affirmation that
c =aleph_1  (i.e. the affirmation that the cardinal of IR is the
smallest strictly greater than the cardinal f IN) is not provable (or
refutable) with the usual axioms of set theory. What confuse you , there?

>
```
 0
Reply denis 12/24/2004 10:53:17 AM

```On Thu, 23 Dec 2004 19:48:08 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

>I'm lost.

Then you have come to the right door!  Come in and join the others.
```
 0
Reply vonroach 12/24/2004 2:41:36 PM

```
vonroach wrote:
> On Tue, 21 Dec 2004 10:40:32 GMT, Fred Bloggs <nospam@nospam.com>
> wrote:
>
>
>>Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?
>
>
> (2 x0)/0 = 2x(0/0)  . there now is that better?

You must be an idiot- we have just finished telling you that 0/0 is not
a number- it is a set. You and that other idiot are merely saying that
if it's a number then it must be a set. Why don't you try demonstrating
some intelligence by showing how the assumption of it must be a set
leads to the conclusion that it must be a number? You won't find one
with your mindless geek symbol manipulation, "nitwit".

```
 0
Reply Fred 12/24/2004 2:58:51 PM

```On Thu, 23 Dec 2004 19:18:24 +0100, Michael Mendelsohn
<invalid@msgid.michael.mendelsohn.de> wrote:

>If in measuring a resistor, we find 0.0A at 0.0V, is the resistance 1
>Ohm, then?

Er...how many resistances have you really measured? Did you read the
instructions carefully?
```
 0
Reply vonroach 12/24/2004 2:59:24 PM

```
vonroach wrote:
> On Tue, 21 Dec 2004 10:37:35 GMT, Fred Bloggs <nospam@nospam.com>
> wrote:
>
>
>>
>>Kevin Aylward wrote:
>>
>>>Fred Bloggs wrote:
>>>
>>>
>>>>Alfred Z. Newmane wrote:
>>>>
>>>>
>>>>>Nicholas O. Lindan wrote:
>>>>>
>>>>>
>>>>>
>>>>>>"John Sefton" <john@petcom.com> wrote
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>0 can't be divided by itself,
>>>>>>
>>>>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>>
>>>>>>It works if the only three numbers in the universe are
>>>>>>0, 1, and infinity -- A number system that seems very
>>>>>>suited to usenet.
>>>>>
>>>>>
>>>>>Except for the fact that: 0 / 0 = undefined
>>>>>
>>>>>Or actually more correct: n / 0 = undefined
>>>>>
>>>>>
>>>>
>>>>0/0={ SET OF ALL INTEGERS }
>>>
>>>
>>>No.
>>>
>>>
>>>
>>>>n/0= NULL SET  for n<>0
>>>>
>>>>It is very well-defined.
>>>
>>>
>>>No it isnt.
>>>
>>>Kevin Aylward
>>
>>You apparently have stumbled on something else you know damn little
>>about. In case you need help with this , you might note that "/" is NOT
>>an operator on the integers, it is the "inverse" of a multiplication
>>operator. Inverse is a well-defined concept but not necessarily a
>>function, it is a set theoretic mapping. E.G. m/n={ q: m=q*n} by
>>definition, so that m/n which is actually a set which can be empty, a
>>singleton, or infinite. In the case of m/n, it is then m/n = F^-1(m)
>>where F(x)= n*x. Your reasoning would lead one to believe /: I x I -> I
>>is a function, which it isn't.
>
>
> Ah, the inverse , like 1/0 is inverse of 0/1?  Is 0/0 the inverse of
> 0/0? And 1/1, the inverse of 1/1.

Inverse in the sense of function preimage, sherlock, and that is a set.
This so-called division operator is really an association of singleton
preimage sets with the number they contain. You can go ahead and make it
an operator if you want, but then you must exclude those Cartesian pairs
with 0 in the denominator- so that "undefined" literally makes sense now.

```
 0
Reply Fred 12/24/2004 3:04:56 PM

```
vonroach wrote:
> On 20 Dec 2004 07:02:45 -0800, merlyn@stonehenge.com (Randal L.
> Schwartz) wrote:
>
>
>>This is a troll.   *Negative*?  Can I have some of the drug you're
>>smoking? :)
>
>
> That's no good Randy, no matter how much you buy, you still have
> nothing. Coincidentally with constant use the measurable IQ approaches
> zero as a limit.

For once I agree with you- several living examples extant here.

```
 0
Reply Fred 12/24/2004 3:07:38 PM

```On Fri, 24 Dec 2004 08:06:07 GMT, Kevin Aylward wrote:
> Dave Seaman wrote:
>> On Thu, 23 Dec 2004 19:02:20 GMT, Kevin Aylward wrote:
>>> Dirk Bruere at Neopax wrote:
>>>> Gordon Weast wrote:
>>
>>
>>>>> Another is renormalization theory in QED (Quantum Electrodynamics).
>>>>> There are several infinities in the theory that appeared to make
>>>>> the results nonsense.  However, if you keep track very carefully,
>>>>> you can get the infinities to cancel and come up with predictions
>>>>> that match measurements very accurately.
>>
>>>> And physicists think it an ugly bodge.
>>
>>> Actually, I think the physicists think its just a bit annoying, its
>>> the mathematicians that think its the ugly bodge.
>>
>> No, not at all.

> Nope.

>>It's not a function in the ordinary sense, but a
>> generalized function.

> Ho hum. What isn't a function? We are discussing QED.

Yes, sorry.  I read in the wrong context.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
```
 0
Reply Dave 12/24/2004 3:20:05 PM

```On Fri, 24 Dec 2004 08:21:39 GMT, Nicholas O. Lindan wrote:
> Referencing:
>> <http://mathworld.wolfram.com/ContinuumHypothesis.html>

> "Dave Seaman" <dseaman@no.such.host> wrote

>> It's a widespread belief (and one that is unfortunately perpetuated by some
>> popular expositions) that the cardinality of the reals is aleph_1.  Not so.
>> The cardinality of the reals is 2^aleph_0, which is the same as
>> aleph_0^aleph_0.  This cardinal is called c, for the cardinality of the
>> continuum.  The proposition that c = aleph_1 is called the continuum
>> hypothesis, and it is known to be independent of the usual axioms of set
>> theory.

> The latter part of the paragraph seems to support the view that
> c = continuum = cardinality of the reals = aleph-0 ^ aleph-0 = aleph^1
> which you claim in the first two sentences to be false.

Perhaps I should have said that the Continuum Hypothesis (CH) is the
"hypothesis" (rather than the "proposition") that c = aleph_1.  The final
clause says that CH is neither provable nor disprovable; that's what
"independent of the axioms" means.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
```
 0
Reply Dave 12/24/2004 3:31:18 PM

```Kevin Aylward wrote:
> Nicholas O. Lindan wrote:
>> "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>>> Nicholas O. Lindan wrote:
>>>> 1 / 0 = oo
>>>> n / 0 = n * oo
>>>> 0 / 0 = 0 * oo = 1
>>>
>>> oo (infinity isn't a number) so you cannot use it this way.
>>
>> Yes, that's my point.  Keep track of oo, don't merge it with
>> numbers.
>>
>> j [sqrt(-1)] isn't a number but we still mix it up with numbers.
>
> Of course it is a number, thats why we treat it as such.

Ok what it's value then?
..
..
..
..
Exactly, it has no defined value.

```
 0
Reply Alfred 12/24/2004 3:57:21 PM

```Alfred Z. Newmane wrote:
> Kevin Aylward wrote:
>> Nicholas O. Lindan wrote:
>>> "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>>>> Nicholas O. Lindan wrote:
>>>>> 1 / 0 = oo
>>>>> n / 0 = n * oo
>>>>> 0 / 0 = 0 * oo = 1
>>>>
>>>> oo (infinity isn't a number) so you cannot use it this way.
>>>
>>> Yes, that's my point.  Keep track of oo, don't merge it with
>>> numbers.
>>>
>>> j [sqrt(-1)] isn't a number but we still mix it up with numbers.
>>
>> Of course it is a number, thats why we treat it as such.
>
> Ok what it's value then?
> .
> .
> .
> .
> Exactly, it has no defined value.

(Was refering to infinity (oo))

```
 0
Reply Alfred 12/24/2004 3:58:30 PM

```Gordon Weast wrote:
> Alfred Z. Newmane wrote:

>>
>>
>> oo (infinity isn't a number) so you cannot use it this way.
>>
>>
>
> Well, if you move out of pure math into something more applied,
> like physics or signal processing, you find a nice little thing
> called the Dirac delta function.  This seems to have confounded
> mathemeticians for a while before they finally came around and
> decided that it really does work.
>
> This wonderful function has infinite height and zero width, yet
> it has area 1.  Granted, you can work with a limit as the width
> goes to 0, but you don't have to.
>
> Think Fourier series and Fourier analysis.  These wouldn't work
> without the Dirac delta function.
>
> A wonderful example of 0 * oo = 1.

Except for the fact it doesn't follow the basic mathematic principal of
0 * n = 0 (anything times zero is zero.) Infinity is undefined. Perhaps
I'm missing something here but how exactly do they get 1 from that?

```
 0
Reply Alfred 12/24/2004 4:08:19 PM

```John Savard wrote:
> On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
> wrote, in part:
>
>> Slightly OT, is there an accepted ASCII-gram for square root?
>
> Here's an example of how I draw equations in ASCII art.
>
>     _
>    /  theta         /  psi     pi \         /  psi     pi \
>   |            sin |  ----- + ---  | + cos |  ----- + ---  |
>   |                 \   2      4  /         \   2      4  /
>   |          ------------------------------------------------- , d psi
>   |                       ____________________________
>   |                      /        2  /  psi     pi \
>   |                     /  1 + tan  |  ----- - ---  |
> _/  0                 \/             \   2      4  /

^^^

What's this zero supposed to represent? The "zero" root? Isn't that
dividing by zero?
n^0 = 1; zeroroot(n) = undefined

What it really comes down to is this:

If
sqrt(4) = 2
can be written as
4^(1/2) = 2,
then
zeroroot(n) = undefined
can be written as
n^(1/0) = undefined,
can it not?

```
 0
Reply Alfred 12/24/2004 4:18:41 PM

```
Alfred Z. Newmane wrote:
> John Savard wrote:
>
>>On Wed, 22 Dec 2004 01:56:47 GMT, "Nicholas O. Lindan" <see@sig.com>
>>wrote, in part:
>>
>>
>>>Slightly OT, is there an accepted ASCII-gram for square root?
>>
>>Here's an example of how I draw equations in ASCII art.
>>
>>    _
>>   /  theta         /  psi     pi \         /  psi     pi \
>>  |            sin |  ----- + ---  | + cos |  ----- + ---  |
>>  |                 \   2      4  /         \   2      4  /
>>  |          ------------------------------------------------- , d psi
>>  |                       ____________________________
>>  |                      /        2  /  psi     pi \
>>  |                     /  1 + tan  |  ----- - ---  |
>>_/  0                 \/             \   2      4  /
>
>
>      ^^^
>
> What's this zero supposed to represent? The "zero" root? Isn't that
> dividing by zero?

It's the lower limit of integration. It's a definite integral between 0
and theta.

```
 0
Reply Fred 12/24/2004 5:18:57 PM

```"Dave Seaman" <dseaman@no.such.host> wrote

> Perhaps I should have said that the Continuum Hypothesis (CH) is the
> "hypothesis" (rather than the "proposition") that c = aleph_1.  The final
> clause says that CH is neither provable nor disprovable; that's what
> "independent of the axioms" means.

Agreed, figured out what I thought you meant, and I think that is what
you thought you meant.

In the original it was hard to tell assertions from negations from
perambulations. It seemed to negate an assertion then assert the first
assertion and conclude that nothing could be asserted or negated.

Did I get that right?

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/24/2004 6:17:17 PM

```"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
> > > j [sqrt(-1)] isn't a number but we still mix it up with numbers.
> > Of course it is a number, thats why we treat it as such.
> Ok what it's value then?

I'm still waiting for a jpeg of quantity sqrt(-1) apples.
I confess my imagination does not stretch this far.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/24/2004 6:22:05 PM

```I read in sci.electronics.design that Nicholas O. Lindan <see@sig.com>
'Is zero even or odd?', on Fri, 24 Dec 2004:
>"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>> > > j [sqrt(-1)] isn't a number but we still mix it up with numbers.
>> > Of course it is a number, thats why we treat it as such.
>> Ok what it's value then?
>
>I'm still waiting for a jpeg of quantity sqrt(-1) apples. I confess my
>imagination do

It seems to me that when you have embraced the concept of -1 apples, the
next step (or half-step back) to j apples, is not so difficult.

Of course, those of us on s.e.d experience the properties of complex
numbers almost every day. Others may not.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/24/2004 6:54:36 PM

```"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>

> What's this zero supposed to represent? The "zero" root? Isn't that
> dividing by zero?
>    n^0 = 1; zeroroot(n) = undefined

Oh, it gets worse.

Conventional disallows 1 / 0
Unconventional allows 1 / 0 and sets it to oo

Expression  Conventional           Unconventional
reduced value   reduced value       Comment

1 / 0        verboten           oo
0^2            0              0 * 0    - is (0 * 0) < or > 0 ?
0^1            0                0
0^0            ?                ?      - is it 0 or is it 1 in either system?
0 - 0          0                ?      - or irreducible or disallowed
0 - 0 - 0      0                ??
0 - (0 - 0)    0                ???

0^0 is a mess in either system.

Aside from 0^0, the conventional system wins in the question mark
race.

Is there a solution to 0 - 0?
Does allowing division by 0 disallow 0 - 0.

Lucky Christmas is upon us.  This is definitely something that can
not be understood unless one is drunk....

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
```
 0
Reply Nicholas 12/24/2004 7:46:25 PM

```On Fri, 24 Dec 2004 18:17:17 GMT, Nicholas O. Lindan wrote:
> "Dave Seaman" <dseaman@no.such.host> wrote

>> Perhaps I should have said that the Continuum Hypothesis (CH) is the
>> "hypothesis" (rather than the "proposition") that c = aleph_1.  The final
>> clause says that CH is neither provable nor disprovable; that's what
>> "independent of the axioms" means.

> Agreed, figured out what I thought you meant, and I think that is what
> you thought you meant.

> In the original it was hard to tell assertions from negations from
> perambulations. It seemed to negate an assertion then assert the first
> assertion and conclude that nothing could be asserted or negated.

> Did I get that right?

I know what I said, but I don't see how I can answer questions about how
it seemed to you.  Such propositions are independent of my axioms.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
```
 0
Reply Dave 12/24/2004 8:06:21 PM

```In article <cfDyd.12532\$ue4.3369@fe12.lga>,
John W. Kennedy <jwkenne@attglobal.net> wrote:
>Nicholas O. Lindan wrote:
>> But the size of the set of real numbers is Aleph 1 (oo^2).
>
>Aleph-1 is at least aleph-null^aleph-null.

But isn't c = 2^aleph-null, and aleph-1 is possibly less than c?

```
 0
Reply russotto 12/24/2004 11:32:07 PM

```"Nicholas O. Lindan" schrieb:
> "Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote
> > When checking it turned out that some thief had actually stolen the
> > resistor where 0V,0A was measured. The circuit was broken, but noone
> > noticed because the voltage was zero.
>
> The circuit wasn't connected.  Therefore no measurement was being
> made.  V = IR has no relevance. R < oo to close the circuit and
> for the equation to apply.

I notice that you're refusing to treat the R = OV/OA quotient like any
other quotient, saying the outcome is "no measurement". In fact, you'd
probably be saying that for any measurement with I=0A since you'd argue
the circuit isn't connected.

But when a mathematician told you that the mathematics "isn't connected"
for n/0, you refused to accept that, even though (to me) the
circumstances are quite identical.

I am hoping that you would take a step back, slap your forehead and say
"Oh, why didn't I see that before?", but it may not happen.

In either case, I wish you happy holidays!
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/24/2004 11:35:14 PM

```In article <tYieQTBX\$6yBFwru@jmwa.demon.co.uk>,
John Woodgate  <noone@yuk.yuk> wrote:
>I read in sci.electronics.design that Matthew Russotto
><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>>John Woodgate  <noone@yuk.yuk> wrote:
>>>I read in sci.electronics.design that Matthew Russotto
>>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>>But sin (pi*x)/pi*x is
>>>>discontinous at zero.
>>>
>>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>>If not, it's 'squeezed'.
>>
>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>
>Squeezed: if the limits are equal, the value of the function at the
>limit point cannot differ from the limit value.

Certainly not a valid theorem.

```
 0
Reply russotto 12/24/2004 11:44:49 PM

```I read in sci.electronics.design that Matthew Russotto
<russotto@grace.speakeasy.net> wrote (in <pt6dnanCFIJsNFHcRVn-
1g@speakeasy.net>) about 'Is zero even or odd?', on Fri, 24 Dec 2004:
>In article <tYieQTBX\$6yBFwru@jmwa.demon.co.uk>,
>John Woodgate  <noone@yuk.yuk> wrote:
>>I read in sci.electronics.design that Matthew Russotto
>><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>>>John Woodgate  <noone@yuk.yuk> wrote:
>>>>I read in sci.electronics.design that Matthew Russotto
>>>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>>>But sin (pi*x)/pi*x is
>>>>>discontinous at zero.
>>>>
>>>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>>>If not, it's 'squeezed'.
>>>
>>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>>
>>Squeezed: if the limits are equal, the value of the function at the
>>limit point cannot differ from the limit value.
>
>Certainly not a valid theorem.
>
Please publish an understandable refutation.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
```
 0
Reply John 12/25/2004 12:38:15 AM

```In article <bpLDMRA3ZLzBFw3L@jmwa.demon.co.uk>,
John Woodgate  <noone@yuk.yuk> wrote:
>I read in sci.electronics.design that Matthew Russotto
><russotto@grace.speakeasy.net> wrote (in <pt6dnanCFIJsNFHcRVn-
>1g@speakeasy.net>) about 'Is zero even or odd?', on Fri, 24 Dec 2004:
>>In article <tYieQTBX\$6yBFwru@jmwa.demon.co.uk>,
>>John Woodgate  <noone@yuk.yuk> wrote:
>>>I read in sci.electronics.design that Matthew Russotto
>>><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>>>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>>>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>>>>John Woodgate  <noone@yuk.yuk> wrote:
>>>>>I read in sci.electronics.design that Matthew Russotto
>>>>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>>>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>>>>But sin (pi*x)/pi*x is
>>>>>>discontinous at zero.
>>>>>
>>>>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>>>>If not, it's 'squeezed'.
>>>>
>>>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>>>
>>>Squeezed: if the limits are equal, the value of the function at the
>>>limit point cannot differ from the limit value.
>>
>>Certainly not a valid theorem.
>>
>Please publish an understandable refutation.

Counterexample:

Consider the function f(x) which is zero at all points except zero, where
it is one.  Now consider the limits of f(x) as x approaches zero from
either side.
```
 0
Reply russotto 12/25/2004 1:39:26 AM

```Matthew Russotto wrote:

> In article <tYieQTBX\$6yBFwru@jmwa.demon.co.uk>,
> John Woodgate  <noone@yuk.yuk> wrote:
>>I read in sci.electronics.design that Matthew Russotto
>><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>>
>>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>>
>>Squeezed: if the limits are equal, the value of the function at the
>>limit point cannot differ from the limit value.
>
> Certainly not a valid theorem.

He's stated it imprecisely and without all the necessary preconditions,
but it certainly *is* a valid theorem; I learned it in freshman
Calculus.

Squeeze Theorem:

If there are three functions, f(x), g(x) and h(x) such that
f(x) >= g(x) >= h(x) over some interval containing a (except
possibly at a itself), and the limit as x goes to a of
f(x) and h(x) are both L, then the limit as x goes to a of
g(x) is L.

--
Christopher Mattern

"Which one you figure tracked us?"
"The ugly one, sir."
"...Could you be more specific?"
```
 0
Reply Chris 12/25/2004 1:09:24 PM

```On Fri, 24 Dec 2004 14:58:51 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

>
>
>vonroach wrote:
>> On Tue, 21 Dec 2004 10:40:32 GMT, Fred Bloggs <nospam@nospam.com>
>> wrote:
>>
>>
>>>Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?
>>
>>
>> (2 x0)/0 = 2x(0/0)  . there now is that better?
>
>You must be an idiot- we have just finished telling you that 0/0 is not
>a number- it is a set. You and that other idiot are merely saying that
>if it's a number then it must be a set. Why don't you try demonstrating
>some intelligence by showing how the assumption of it must be a set
>leads to the conclusion that it must be a number? You won't find one
>with your mindless geek symbol manipulation, "nitwit".

Your abstract imagination has led you to a state of hubris. Worse, you
are relying on half forgotten abstract thoughts of others.  0 is a
number symbol, though western counters were not smart enough to
realize it.  Division by 0 is undefined, thus it is a meaningless
concept. Infinity is a real and important concept. It is vital to
`Differentiation'. It is an ambiguous concept unless defined. There is
not just one `infinity'.
```
 0
Reply vonroach 12/26/2004 6:52:45 AM

```"Nicholas O. Lindan" schrieb:
> "Shawn Corey" <shawn.corey@sympatico.ca> wrote
> >           a = b
[..]
> >           2 = 1
>
> Now if we can just get the IRS to agree.

Posted on alt.humor.best-of-usenet:

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/27/2004 12:23:07 AM

```
Nicholas O. Lindan wrote:

> "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote
>
>>>>j [sqrt(-1)] isn't a number but we still mix it up with numbers.
>>>
>>>Of course it is a number, thats why we treat it as such.
>>
>>Ok what it's value then?
>
>
> I'm still waiting for a jpeg of quantity sqrt(-1) apples.
> I confess my imagination does not stretch this far.
>

It's over here, right next to my picture of -1 apples...

That's even a real integer, equally as hard to picture.
```
 0
Reply Gordon 12/27/2004 3:32:10 PM

```Gordon Weast schrieb:
> It's over here, right next to my picture of -1 apples...

With all those digital cameras around nowadays, most people seem to have
forgotten about photographic negatives. ;)

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/27/2004 8:00:03 PM

```"Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote in message
news:41D069C3.FF9AFE3@msgid.michael.mendelsohn.de...
> Gordon Weast schrieb:
> > It's over here, right next to my picture of -1 apples...
>
> With all those digital cameras around nowadays, most people seem to have
> forgotten about photographic negatives. ;)

But with digital images, it is possible to show the bit-wise negation of an
image of an apple.

```
 0
Reply Richard 12/27/2004 8:31:00 PM

```Groan.....  8-)

Richard Henry wrote:

> "Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote in message
> news:41D069C3.FF9AFE3@msgid.michael.mendelsohn.de...
>
>>Gordon Weast schrieb:
>>
>>>It's over here, right next to my picture of -1 apples...
>>
>>With all those digital cameras around nowadays, most people seem to have
>>forgotten about photographic negatives. ;)
>
>
> But with digital images, it is possible to show the bit-wise negation of an
> image of an apple.
>
>
>
```
 0
Reply Gordon 12/27/2004 9:00:46 PM

```Richard Henry schrieb:
> "Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote in message
> > Gordon Weast schrieb:
> > > It's over here, right next to my picture of -1 apples...
> >
> > With all those digital cameras around nowadays, most people seem to have
> > forgotten about photographic negatives. ;)
>
> But with digital images, it is possible to show the bit-wise negation of an
> image of an apple.

Hmm, I'm not 100% sure, but if I multiply i to the coordinates of every
pixel, given as x+iy, isn't the picture rotated?
i apple is then 1 apple rotated.

Cheers
Michael
--
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
```
 0
Reply Michael 12/27/2004 10:06:28 PM

```
vonroach wrote:
> On Fri, 24 Dec 2004 14:58:51 GMT, Fred Bloggs <nospam@nospam.com>
> wrote:
>
>
>>
>>vonroach wrote:
>>
>>>On Tue, 21 Dec 2004 10:40:32 GMT, Fred Bloggs <nospam@nospam.com>
>>>wrote:
>>>
>>>
>>>
>>>>Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?
>>>
>>>
>>>(2 x0)/0 = 2x(0/0)  . there now is that better?
>>
>>You must be an idiot- we have just finished telling you that 0/0 is not
>>a number- it is a set. You and that other idiot are merely saying that
>>if it's a number then it must be a set. Why don't you try demonstrating
>>some intelligence by showing how the assumption of it must be a set
>>leads to the conclusion that it must be a number? You won't find one
>>with your mindless geek symbol manipulation, "nitwit".
>
>
> Your abstract imagination has led you to a state of hubris. Worse, you
> are relying on half forgotten abstract thoughts of others.  0 is a
> number symbol, though western counters were not smart enough to
> realize it.  Division by 0 is undefined, thus it is a meaningless
> concept.

Apparently you can't pick up on "0/0" being a symbol- call it @#\$%^&*,
which has been shown to be the set of all numbers.

>Infinity is a real and important concept. It is vital to
> `Differentiation'. It is an ambiguous concept unless defined. There is
> not just one `infinity'.

No- it is the idea of a continuum that is more important here. I see
nothing relevant in all these various degrees of infinity that has
anything to do with differentiation.

```
 0
Reply Fred 12/27/2004 11:19:25 PM

```Fred Bloggs wrote:
>
> Apparently you can't pick up on "0/0" being a symbol- call it @#\$%^&*,
> which has been shown to be the set of all numbers.

Are you claiming that

0/0 = set of all numbers

?  Because if you are you are wrong.
```
 0
Reply George 12/28/2004 12:51:30 AM

```
George Cox wrote:
> Fred Bloggs wrote:
>
>>Apparently you can't pick up on "0/0" being a symbol- call it @#\$%^&*,
>>which has been shown to be the set of all numbers.
>
>
> Are you claiming that
>
>    0/0 = set of all numbers
>
> ?  Because if you are you are wrong.

Ookay- thnx for the insight.

```
 0
Reply Fred 12/28/2004 2:25:35 PM

```
"Vince Fiscus, KB7ADL" wrote:

> Gactimus <gactimus@xrs.net> wrote in news:10sdnunotbnere2@corp.supernews.com:
>
> > I know 0 is neither negative or positive but what about odd/even? I think
> > it's even.
> >
> > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
> > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8
>
> An even number plus an even number equals an even number.
>
> An odd number plus an even number equals an odd number.
>
> An odd number plus an odd number equals an even number.
>
> 0 + 1 = odd number
>
> 0 + 2 = even number,  2 is not odd, so zero must be even.
>

Dont ever say "must".  Thatw as inthe Novice exam!

```
 0
Reply ISU 12/29/2004 4:59:57 AM

```Androcles wrote:
>
> When I was test engineering for flight simulators, the DC9 sits
>[SNIP]

fascinating!

```
 0
Reply Andrew 1/4/2005 11:01:44 PM

```Maybe it's nothing!

"Andrew Hamm" <ahamm@mail.com> wrote in message
news:340lisF43djv0U2@individual.net...
> Androcles wrote:
>>
>> When I was test engineering for flight simulators, the DC9 sits
>>[SNIP]
>
> fascinating!
>
>
>

```
 0
Reply crzndog 1/5/2005 2:18:15 AM

```http://www.a18dy.googlepages.com/0.htm 街头行为艺术
```
 0
Reply hpswlp1 (9) 3/25/2007 6:18:45 PM

```http://uminonm.googlepages.com/0.htm 搞笑的情书
```
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Reply hpswlp1 (9) 3/28/2007 4:05:15 PM

```http://maobra.googlepages.com/0.htm 未来十大灾难的神秘预言
```
 0
Reply aibbyun (8) 3/30/2007 11:48:19 AM

```http://xnlihua.googlepages.com/0.htm 加油陷阱
```
 0
Reply aibbyun (8) 4/1/2007 10:33:12 AM

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```
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Reply maobra (1) 4/2/2007 10:55:20 AM

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Not very long ago, I posted some request for comments about a vector, which would have been a collection of variables like the array, but with a defined range of integers as indices into an (C-)array instead of the hashtable. Interest within c.l.t wasn't noticeable, and the real use (speedup of direct access and iteration by sorted index) isn't really estimateable without a prototype implementation. This weekend, I tried my own hands on it, and got stuck pretty soon. What bit-value to use for a new "VAR_VECTOR". The "flags" field is an "int", and so fa...

Save As acting oddly
1.Setting: CD boxed PSP8 with patch, 512 memory, 20G free space WinXPsp1/2 etc. No PSP8 workspaces 2. Open a saved image, select, copy, paste as a new image etc and proceed to do layers, merge. 3.Click on Save As in the File menu and the usual pop up box routine results allowing the name and the ordinary .jpg file type. (Appears saved) 4.Go to close that image and the question 'Do you want to save this?' results and the image on the screen still retains a no name property e.g. 'image2' . 5.If I say yes and redo the naming routine the message says it already exists BUT an inspec...

find zero values of sinc
hi all: i want to find the zero values of sinc, where sinc = sin(pi*x)./(pi*x) x = -5.5:0.1:5.5; sinc = sin(pi*x)./(pi*x); plot(x, sinc) you can clearly see the zero crossings, but find(sinc == 0) is null (i think) because i've discretized a continuous function, and none of the values are exactly zero. then i tried to convert sinc into a continuous function: mysinc = @(x)sin(pi*x)./(pi*x) (don't ask me why i didn't type mysinc = 'sin(pi*x)./(pi*x)'; instead, because i learn by example) this is where i get stuck. matlab seems to have good ways to find the roots of ...

Odd result from lib\$sub_times
Using lib\$sub_times to subtract times. if I subtract 0 from 1 I get -1 If I subtract 0 for 0 I get -1 Makes no sense to me. It seems to give the wrong answer if the times are identical. On 2013-08-12 19:10:04 +0000, Tom Adams said: > Using lib\$sub_times to subtract times. > > if I subtract 0 from 1 I get -1 > If I subtract 0 for 0 I get -1 > > Makes no sense to me. It seems to give the wrong answer if the times > are identical. I smell a corner case. Per the documentation, entering two absolute times always produces a delta time. In VMS, ze...

Zero Padding Circuit Design
Hi all, i want to design a zero padding circuit. The problem is the number of zero depends on the number of input data. Let's say i have 2000 data input, the number of output data should be divided by factor of 600. So number of zero padding = 400 --> (2000+400)/600 = integer value Remember that number of data input could vary, so it will change the number of zero padding Can you give me suggestion, how to implement zero padding circuit in hardware? *I plan to design the circuit 10 port parallely, so for above example, it will need 200 clock to input all data. ...

Odd REQ: Act! for Mac
Hey there, Does anyone have the most recent version of Act! for Mac (even if it's for Classic only)? Thanks in advance! -GK In article <2007011816570875249-northwest@mailinatorcom>, George Kaplan <northwest@mailinator.com> wrote: > Hey there, > > Does anyone have the most recent version of Act! for Mac (even if it's > for Classic only)? > > Thanks in advance! > -GK AFAIK, there never was an ACT! for MacOS. According to http://www.act.com/ ACT! was a contact manager. There are a bunch MacOS contact managers. The one I've heard about ...

sas format for BLANK when ZERO
last year Mike had the solution below. this works fine on PC but not on MAINFRAME does someone has an idea why not?? or another proposal? H.. -------------------------------------------------------------------------------------------------------- data test; input val @@; cards; 1 2 0 3 0.00 4 0.000 5 10000 2010 ; run; proc format; value zer 0 = ' ' other = [comma20.2] ; run; proc print data=test; format val zer.; run; Obs val 1 1.00 2 2.00 3 4 3.00 5 6 4.00 7 8 5.00 9 10...

List Separator \$, behaving oddly
hello all, when we set the \$, punctuation variable two different ways we get different behaviors. perl -e ' # this does not work local *{"::,"} = \do{q[:]}; print "\\$,=[\$,]\n"; print "A", "B", "C"; #<--- ABC are not separated by colon, even though \$, is set to a colon. printf "\n"; '; perl -e ' # this works local \${*{"::,"}} = q[:]; print "\\$,=[\$,]\n"; print "A", "B", "C"; #<--- A:B:C are colon separated & ok. printf "\n"; '; ...

Odd data structure help
I have, over the past few years, developed a Access system that is in use in our companies engineering, purchasing, and sales departments. It is a fairly complex system that runs great. So, I am pretty well versed in Access design (many thanks to all the posters in this group too, I'm not sure I could have done without). I do have a situation that has stumped me though. I have a table listing various parts that are used for a "quote list" (tblPartsTemplate). The list is getting too long to sort through manually so I am trying to add some pre-set filters. In the form where the &...

relsize.sty and zero tolerance
relsize.sty behaves strangely if \RSpercentTolerance is set to 0 which is recommended in the manual. In line 101 of relsize.sty the check is done for executing the size adjustment when the requested size deviates more than \RSpercentTolerance from a preset size: \ifnum\@tempdima>\RSpercentTolerance The problem is that \@tempdima can get negative if the requested size is smaller than a preset size and doesn't get scaled. Thus if the user wants zero tolerance, he gets unpredictable 0 or 1% tolerance. So an additional check is needed whether \RSpercentTolerance i...

PN SEQUENCE (zero values)
just for check IS there any way to produce a PN sequence from all zero intial state. that is all zeros in shift regiters On Feb 4, 3:19=A0pm, "Avier" <shahanwark...@hotmail.com> wrote: > just for check > > IS there any way to produce a PN sequence from all zero =A0intial state. > > that is all zeros in shift regiters I believe the all-zeros state is never legal because it would cause all subsequent outputs to be zero. >On Feb 4, 3:19=A0pm, "Avier" <shahanwark...@hotmail.com> wrote: >> just for check >> &g...

argparse zero-length switch
Is it possible to specify a zero-length switch? Here's what I mean. I have a use case where some users would have to enter a section name on th= e command line almost every time, whereas other users (the ones using only = one section) will never have to enter the section name. I don't want to bu= rden users with only one "section" to always enter the section name as a re= quired argument, but I also want to make it as convenient as possible to en= ter the section name for those who need to. My thought, on the thinking that practicality beats purity, was to create a= zero...

herding ones and zeroes into bytes
I continue to try to implement a black word/white word encoding similar to the treatment given in chp. 18 of _unleashed_. #include <stdio.h> #include <stdlib.h> #define PATH "george.txt" #define NUMBER 100 #define MAXFMTLEN 2000 int main(void) { FILE *fp; char pattern[MAXFMTLEN]; char lbin[NUMBER]; char line[MAXFMTLEN]; if ((fp = fopen(PATH, "r")) == NULL ) { fprintf(stderr, "can't open file\n"); exit(1); } sprintf(pattern, "%%*s %%%ds", NUMBER-1); while(fgets(line, MAXFMTLEN, fp) == line){ sscanf(...

Odd question bout Prolog
Hi guys, I'm trying to do a report, but I'm having problems finding information about Prolog. Basically, what I'm struggling with is finding negative aspects of Prolog: limitations, restrictions, poor features, etc. I'm supposed to right about it's comparison with Lisp for the purpose of AI applications, but again... I'm struggling. If anyone could offer any insight.. I'd appreciate tremendously. On 18 Sep 2004 17:11:56 -0700, sap6210@rit.edu wrote: >Hi guys, I'm trying to do a report, but I'm having problems finding >information about Prolog. ...