Is zero even or odd?

[Peter Wyzl]

"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...

 

[Vince Fiscus, KB7ADL]

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.



KB7ADL

 

[Richards Noah (IFR LIT ME]

"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.

 

[John Woodgate]

I read in sci.electronics.design that Matthew Russotto
<russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
jg@speakeasy.net&gt 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

 

[Michele Dondi]

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,

 

[Bill Smythe]

"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

 

[vonroach]

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.

 

[vonroach]

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.

 

[vonroach]

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?

 

[vonroach]

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?

 

[vonroach]

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.

 

[vonroach]

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.

 

[vonroach]

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?

 

[vonroach]

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.

 

[robert j. kolker]

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

 

[Paul Burke]

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

 

[robert j. kolker]

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

 

[David Kastrup]

"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

 

[Shawn Corey]

vonroach wrote:

Then infinity is undefined?

Infinity is defined but not a number.

infinity = limit(x->0) 1/x^2

--- Shawn

 

[Alfred Z. Newmane]

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.