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Topic: 0^0=1
Replies: 145   Last Post: Jun 5, 2012 1:10 PM

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Ross Clement

Posts: 85
Registered: 1/25/05
Re: 0^0=1
Posted: May 7, 2012 4:51 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 21, 4:23 am, "DonH" <donlhumphr...@bigpond.com> wrote:
> "Richard Tobin" <rich...@cogsci.ed.ac.uk> wrote in message
>
> news:jmsvh1$nml$1@matchbox.inf.ed.ac.uk...
>

> > In article
> > <fc51d462-6ab6-4087-97c1-63bda0170...@fv28g2000vbb.googlegroups.com>,
> > Tonico  <Tonic...@yahoo.com> wrote:

>
> >>Or, since we're dealing with real or complex numbers, consider lim x^x
> >>= lim e^{x log(x)} , when x --> 0 ...this is a good reason to define
> >>0^0 = 1 .

>
> > But equally one could consider the limit of 0^x.
>
> > For integers the set mapping argument seems compelling, but when
> > dealing with the reals it seems better to leave it undefined or define
> > it explicitly if needed.

>
> > -- Richard
>
> # Yes, 0^0 may be an arbitrary device to accommodate a computer, as Barron's
> Maths Study Dictionary excludes zero(^0) (pg.62) when defining the "zero
> exponent".
>     Which still leaves, eg. 5^0 = 1.
>      If I have five apples and multiply them by themselves zero times, do I
> end up with one apple?
>      Also, does 5^0 = 5 * 1/5?
>      Has x^0 = 1 ever been proved?  Or, is it merely a convenient dogma?


I'm not a mathematician, and I can't read all 380 posts in this
thread.

But, my understanding of the reason that x^0 = 1 is a consequence of
negative exponents. E.g.

if 2^-2 equals 1/2^2 and x^a * x^b = x^(a+b), then 2^2 * 2^-2 = 2^(2 +
-2) = 2^0.

We can then expand the example to get 2^0 = 2^2 * 1/(2^2) = 1.

However, if x = 0, then the derivation of a^0 = 1 no longer works:

0^2 * 0^-2 = 0*0 / (0*0) = 0/0 which is undefined.

Hence x^0 = 1 is based on a derivation that doesn't work for x=0, and
hence to quote the consequence of that derivation to argue the value
of 0^0 is plain wrong.

I presume that I'm "missing something" and someone will be along to
spank me soon.


Date Subject Author
4/20/12
Read 0^0=1
Don H
4/20/12
Read Re: 0^0=1
Virgil
4/20/12
Read Re: 0^0=1
Pubkeybreaker
4/20/12
Read Re: 0^0=1
J. Antonio Perez M.
4/20/12
Read Re: 0^0=1
Richard Tobin
4/20/12
Read Re: 0^0=1
Don H
4/21/12
Read Re: 0^0=1
LudovicoVan
4/21/12
Read Re: 0^0=1
Peter Webb
4/21/12
Read Re: 0^0=1
Dave Dodson
4/21/12
Read Re: 0^0=1
Peter Webb
4/21/12
Read Re: 0^0=1
Don H
4/21/12
Read Re: 0^0=1
Frederick Williams
4/21/12
Read Re: 0^0=1
Don H
4/21/12
Read Re: 0^0=1
Frederick Williams
4/21/12
Read Re: 0^0=1
Bart Goddard
4/22/12
Read Re: 0^0=1
Don H
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/22/12
Read Re: 0^0=1
Bart Goddard
4/22/12
Read Re: 0^0=1
Virgil
4/23/12
Read Re: 0^0=1
Frederick Williams
4/23/12
Read Re: 0^0=1
Pubkeybreaker
4/23/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Dave Dodson
4/22/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/22/12
Read Re: 0^0=1
Peter Webb
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/23/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Frederick Williams
5/7/12
Read Re: 0^0=1
Ross Clement
5/7/12
Read Re: 0^0=1
LudovicoVan
5/7/12
Read Re: 0^0=1
exmathematician
5/7/12
Read Re: 0^0=1
Ki Song
5/7/12
Read Re: 0^0=1
LudovicoVan
5/7/12
Read Re: 0^0=1
Ki Song
5/7/12
Read Re: 0^0=1
LudovicoVan
5/7/12
Read Re: 0^0=1
Ki Song
5/10/12
Read Re: 0^0=1
Michael Stemper
5/7/12
Read Re: 0^0=1
Frederick Williams
5/7/12
Read Re: 0^0=1
LudovicoVan
5/8/12
Read Re: 0^0=1
Butch Malahide
5/8/12
Read Re: 0^0=1
LudovicoVan
5/8/12
Read Re: 0^0=1
Ross Clement
5/8/12
Read Re: 0^0=1
Jussi Piitulainen
5/7/12
Read Re: 0^0=1
Ross Clement
5/8/12
Read Re: 0^0=1
Frederick Williams
5/8/12
Read Re: 0^0=1
Ki Song
5/8/12
Read Re: 0^0=1
David W. Cantrell
5/8/12
Read Re: 0^0=1
Dan Christensen
5/8/12
Read Re: 0^0=1
Frederick Williams
5/8/12
Read Re: 0^0=1
Dan Christensen
5/8/12
Read Re: 0^0=1
William Hale
5/8/12
Read Re: 0^0=1
Dan Christensen
5/9/12
Read Re: 0^0=1
Frederick Williams
5/10/12
Read Re: 0^0=1
Michael Stemper
5/10/12
Read Re: 0^0=1
Dan Christensen
5/9/12
Read Re: 0^0=1
Frederick Williams
5/9/12
Read Re: 0^0=1
Dan Christensen
5/9/12
Read Re: 0^0=1
LudovicoVan
5/10/12
Read Re: 0^0=1
Michael Stemper
5/8/12
Read Re: 0^0=1
Dan Christensen
5/8/12
Read Re: 0^0=1
Frederick Williams
5/22/12
Read Re: 0^0=1
Michael Press
5/28/12
Read Re: 0^0=1
address_is@invalid.invalid
5/28/12
Read Re: 0^0=1
address_is@invalid.invalid
6/5/12
Read Re: 0^0=1
Michael Press
4/21/12
Read Re: 0^0=1
David C. Ullrich
4/21/12
Read Re: 0^0=1
G. A. Edgar
4/23/12
Read Re: 0^0=1
David C. Ullrich
4/25/12
Read Re: 0^0=1
Shmuel (Seymour J.) Metz
4/26/12
Read Re: 0^0=1
Helmut Richter
4/21/12
Read Re: 0^0=1
LudovicoVan
4/21/12
Read Re: 0^0=1
Richard Tobin
4/21/12
Read Re: 0^0=1
Efftard K. Donglemeier
4/22/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Don H
4/22/12
Read Re: 0^0=1
Bart Goddard
4/23/12
Read Re: 0^0=1
harold james
4/23/12
Read Re: 0^0=1
Don H
4/24/12
Read Re: 0^0=1
Bart Goddard
4/24/12
Read Re: 0^0=1
Frederick Williams
4/24/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
Pfsszxt@aol.com
4/22/12
Read Re: 0^0=1
Wally W.
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/22/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Jussi Piitulainen
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Jussi Piitulainen
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Frederick Williams
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Jussi Piitulainen
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Jussi Piitulainen
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Frederick Williams
4/23/12
Read Re: 0^0=1
Dan Christensen
4/24/12
Read Re: 0^0=1
Frederick Williams
4/25/12
Read Re: 0^0=1
Shmuel (Seymour J.) Metz
4/25/12
Read Re: 0^0=1
Dan Christensen
4/25/12
Read Re: 0^0=1
Frederick Williams
4/25/12
Read Re: 0^0=1
Dan Christensen
4/25/12
Read Re: 0^0=1
Rotwang
4/25/12
Read Re: 0^0=1
Dan Christensen
4/25/12
Read Re: 0^0=1
Frederick Williams
4/25/12
Read Re: 0^0=1
Dan Christensen
4/25/12
Read Re: 0^0=1
Jussi Piitulainen
4/25/12
Read Re: 0^0=1
David W. Cantrell
4/25/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Jussi Piitulainen
4/26/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Rotwang
4/26/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Dan Christensen
4/25/12
Read Re: 0^0=1
Frederick Williams
4/25/12
Read Re: 0^0=1
Jussi Piitulainen
4/25/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Jussi Piitulainen
4/26/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Jussi Piitulainen
4/26/12
Read Re: 0^0=1
Dan Christensen
4/27/12
Read Re: 0^0=1
Jussi Piitulainen
5/22/12
Read Re: 0^0=1
Michael Press
5/22/12
Read Re: 0^0=1
Kaba
5/23/12
Read Re: 0^0=1
Michael Press
4/23/12
Read Re: 0^0=1
Frederick Williams
4/27/12
Read Re: 0^0=1
Frederick Williams
4/26/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Dan Christensen
4/27/12
Read Re: 0^0=1
Frederick Williams
4/27/12
Read Re: 0^0=1
Dan Christensen
4/27/12
Read Re: 0^0=1
Repeating Rifle
4/27/12
Read Re: 0^0=1
jbriggs444@gmail.com
4/28/12
Read Re: 0^0=1
Repeating Rifle
4/28/12
Read Re: 0^0=1
Dan Christensen
4/28/12
Read Re: 0^0=1
Frederick Williams
4/28/12
Read Re: 0^0=1
Tim Little
4/27/12
Read Re: 0^0=1
Shmuel (Seymour J.) Metz
4/29/12
Read Re: 0^0=1
Dr J R Stockton
4/29/12
Read Re: 0^0=1
David W. Cantrell

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