Is zero even or odd?

[Alfred Z. Newmane]

John Woodgate wrote:

I read in sci.electronics.design that Alfred Z. Newmane
a.newmane.remov e@eastcoastcz.com> wrote (in
33dkokF3vfnfcU1@individual.net&gt about 'Is zero even or odd?', on
Tue, 28 Dec 2004:
I've checked every calc I could find with a power function to verify
this. Any graphing type calc yeilds some sort of DOMAIN error, and
any sci calc I've tried simply gives a generic error.

Could it be that we are discussing pure mathematics, not calculators,
or Ohm's Law, or the price of imaginary apples?

I was using to prove a point of pure mathematics, that 0^0 is undefined
(out of the valid domain.)

 

[Keith Williams]

In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
dseaman@no.such.host says...

On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
dseaman@no.such.host says...

Well, 0^0 is a mess. But lim x->0 0^x is well defined.

No, it isn't. That limit does not exist.

Most certainly does. It's zero.

Wrong. That limit cannot exist because 0^x is undefined for all x < 0.

"lim x->0 0^x "

Where is X < 0 in the above?

Look up the definition of limit. Notice that "limit" in the reals means
"two-sided limit." In particular, that means the left-hand and
right-hand limits must both exist, and must agree.

Ah, so the lim x->oo 1/x is?

--
Keith

 

[Dave Seaman]

On Tue, 28 Dec 2004 11:15:07 -0800, Alfred Z. Newmane wrote:

Dave Seaman wrote:

But correct me if I'm wrong, isn't returning 1 from 0^0 /mathematically/
incorrect? I have always known that to be out of the valid domain for
n^0.

I take it you haven't been reading the thread, since I have given several
mathematical arguments and provided references to support the conclusion
that 0^0 = 1.


--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>

 

[Scott Seidman]

Dave Seaman <dseaman@no.such.host> wrote in news:cqshg3$q87$1
@mailhub227.itcs.purdue.edu:

Ah, so the lim x->oo 1/x is?

Doesn't exist, because the one-sided limits don't agree.

Well, that wipes out all the math I ever learned. I guess all that calc
I took in college was for naught.

Did those calc courses teach you that there is a +infinity and a
-infinity?

But wouldn't "both sides" of the limit as x -> infinity be referring to
infinity+ and infinity-? This is rather different from saying the limit as
x goes to minus infinity is not the same as the limit as x approaches plus
infinity-- the latter does not refer to both sides of the limit

Scott

 

[vonroach]

On Tue, 28 Dec 2004 09:44:55 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:

vonroach wrote:
On Tue, 28 Dec 2004 04:56:23 +0000 (UTC), Dave Seaman
dseaman@no.such.host> wrote:

No, it isn't. That limit does not exist.
But 0^0 does exist and has nothing to do with limits.

Only in your mind.

Here you go again.

0^0 is undefined.

Check back when you are awake.

 

[vonroach]

On Tue, 28 Dec 2004 11:05:22 -0600, John Fields
<jfields@austininstruments.com> wrote:

How comforting it must be for you to know that somewhere, on a dusty
old bookrack, lies a little book which releases you from the drudgery
of thinking.


John Fields
Sorry Johnny if you are going to indulge in abstractions, you have to

observe the rules.

 

[vonroach]

On Tue, 28 Dec 2004 09:46:05 -0600, russotto@grace.speakeasy.net
(Matthew Russotto) wrote:

But 0^0 does exist and has nothing to do with limits.

0^0 can be defined by convention, of course, as is 0 factorial.

No you can't go that route either.

 

[vonroach]

On Tue, 28 Dec 2004 16:09:56 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> wrote:

I consider it to be something more than a mere convention. In Suppes:
_Axiomatic Set Theory_, it's a *theorem* that m^0 = 1 for every cardinal
m. Since 0 is a cardinal, the corollary is that 0^0 = 1. Specifically,
it represents the cardinality of the set of mappings from the empty set
to itself.

Chuckle, except for the fact that 0^0 is meaningless undefined babble.
n^0 = 1 where n is a positive number, not equal to 0.

 

[vonroach]

On Tue, 28 Dec 2004 09:51:12 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:

2^0 = 1
1^0 = 1
0^0 = ERROR, DOMAIN (hence the limit)
(-1)^0 = 1
(-2)^0 = 1

(-1^1/2)^0 =?
or ( i )^0 =?

 

[vonroach]

On Tue, 28 Dec 2004 18:14:54 +0000, John Woodgate
<jmw@jmwa.demon.contraspam.yuk> wrote:

Could it be that we are discussing pure mathematics, not calculators, or
Ohm's Law, or the price of imaginary apples?
--
It was never made clear whether the `apple' in question was a fruit

or a computer.

 

[vonroach]

On Tue, 28 Dec 2004 10:29:36 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:

I was using to prove a point of pure mathematics, that 0^0 is undefined
(out of the valid domain.)

Didn't you know that?

 

[vonroach]

On Tue, 28 Dec 2004 18:21:18 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> wrote:

The Macintosh calculator returns 1. So do most Hewlett-Packard calculators
that I have tried, and at least one by Texas Instruments that I can recall.
Likewise Maple and MATLAB (but not Mathematica).

You rely on a computer? How slipshod.

 

[vonroach]

On Tue, 28 Dec 2004 19:27:01 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> wrote:

I take it you haven't been reading the thread, since I have given several
mathematical arguments and provided references to support the conclusion
that 0^0 = 1.

None of which have been accepted.

 

[George Cox]

John Fields wrote:

Then what would be the proper way to write it, please?

Write what? That 1/x gets big as x gets small?

1/x -> +infinity as x -> +0

1/x -> -infinity as x -> -0.

 

[ISU WINS!]

"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.

KB7ADL

Dont ever say "must". Thatw as inthe Novice exam!

 

[vonroach]

On Tue, 28 Dec 2004 22:16:07 -0000, "George Dishman"
<george@briar.demon.co.uk> wrote:

The task at hand is to show whether the rule
is valid or otherwise. Can you do that?

Otherwise? Accept your opinion? Crazy George is really crazy!

 

[vonroach]

On Tue, 28 Dec 2004 22:04:23 -0000, "George Dishman"
<george@briar.demon.co.uk> wrote:

Not really, simply cooling a resistive material
won't usually reduce the resistance to zero. The
superconducting state is fundamentally different.

Ah, another subject where you are poorly informed.

 

[vonroach]

On Tue, 28 Dec 2004 22:13:54 -0000, "George Dishman"
<george@briar.demon.co.uk> wrote:

0 = k * 0
What a profound observation. How many years have you ben working on

this concept? I suppose k*k= k^2 will be next? Have you carefully
assured yourself that 1+1=2?

 

[vonroach]

On Tue, 28 Dec 2004 17:08:26 -0600, John Fields
<jfields@austininstruments.com> wrote:

Ah, but the normal order of precedence dictates that the
multiplication be performed first,

Parentheses and exponents are dealt with first.

 

[vonroach]

On Wed, 29 Dec 2004 01:06:32 +0100, Michael Mendelsohn
<invalid@msgid.michael.mendelsohn.de> wrote:

So (k*0)/0 is not equal to k*(0/0), then?
What a pity!

Both are meaningless and undefined.