Is zero even or odd?

[David Kastrup]

"Nicholas O. Lindan" <see@sig.com> writes:

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

It gives us, for example,
1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2

Well, that's wrong. Obviously wrong. But constructing
a false statement doesn't have much value that I can see.

Well, so we better not define things leading to false statements.

Try:
0 + 0 = 2 * 0 <> 0
1 = 0/0

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

The only definition that does not result in contradictions is that
0/0 is 'any number'. 1 is just one solution.

I'll buy it.

You buy 0+0 <> 0? Uh, 0+x = x+0 = x is the _definition_ of 0. If you
buy 0+0 <> 0, you'll buy anything.

To say 'it is not defined' is as to say 'here there be monsters',
and suddenly everybody (most everbody, well, would you believe >0)
wants to go there. It is the undiscovered country.

0/0 is the undiscovered country? I recommend that you take a pair of
knitting needles and stick them with your bare hands into the next
electric outlet. That will give you some more exciting "undiscovered
country". Not everything that is a proven bad idea is "undiscovered".

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum

 

[Alfred Z. Newmane]

vonroach wrote:

On Fri, 31 Dec 2004 09:11:43 -0800, "Alfred Z. Newmane"
a.newmane.remove@eastcoastcz.com> wrote:

What in the sam-hell are you on? Thats what I've /BEEN/ saying, ya
trollimous maximus;

I've been saying it's undefined.

Then there was the trifle of your ambiguous apple question or should I
say troll.

I never asked the apple question, that was someone else. No wonder
you're so mixed up, you can't even put a statement with the correct
name!

 

[Alfred Z. Newmane]

Earle Jones wrote:

In article <34d3vdF47dpkeU1@individual.net>,
"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote:

vonroach wrote:
On Fri, 31 Dec 2004 09:11:43 -0800, "Alfred Z. Newmane"
a.newmane.remove@eastcoastcz.com> wrote:

What in the sam-hell are you on? Thats what I've /BEEN/ saying, ya
trollimous maximus;

I've been saying it's undefined.

Then there was the trifle of your ambiguous apple question or
should I say troll.

I never asked the apple question, that was someone else. No wonder
you're so mixed up, you can't even put a statement with the correct
name!

*
Zero is even.

1. It is divisible by two without a remainder.
2. It occurs between two odd integers.

earle
*

Exactly. And if I may expand on that:

Remember that:
even + even = even (eg: 2 + 4 = 6)
and
odd + even = odd (eg: 2 + 3 = 5)
and
odd + odd = even (eg: 3 + 5 = 8)


Consider:
0 + 2 = 2
- Even result, so zero must be Even; e+e=e rule.
But:
0 + 1 = 1
- Odd result, so 0 cannot be odd.
- Follows the e+o=o rule, again showing 0 must be Even.

 

[Earle Jones]

In article <34d3vdF47dpkeU1@individual.net>,
"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com> wrote:

vonroach wrote:
On Fri, 31 Dec 2004 09:11:43 -0800, "Alfred Z. Newmane"
a.newmane.remove@eastcoastcz.com> wrote:

What in the sam-hell are you on? Thats what I've /BEEN/ saying, ya
trollimous maximus;

I've been saying it's undefined.

Then there was the trifle of your ambiguous apple question or should I
say troll.

I never asked the apple question, that was someone else. No wonder
you're so mixed up, you can't even put a statement with the correct
name!

*
Zero is even.

1. It is divisible by two without a remainder.
2. It occurs between two odd integers.

earle
*