Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Formal proof of the ambiguity of 0^0
Replies: 163   Last Post: Nov 13, 2013 10:45 AM

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: Formal proof of the ambiguity of 0^0
Posted: Oct 17, 2013 6:07 PM

On Thursday, October 17, 2013 10:09:01 AM UTC-4, Dan Christensen wrote:
> On Thursday, October 17, 2013 6:28:33 AM UTC-4, Bart Goddard wrote:
>

> > Dan Christensen <Dan_Christensen@sympatico.ca> wrote in
>
> >
>
>
> >
>
> >
>
> >
>
> > > To follow-up on my previous postings at sci.math
>
> >
>
> >
>
> >
>
> > ...because you think garbage will evolve into real
>
> >
>
> > mathematics if you just keep repeating it...?
>
> >
>
> >
>
> >
>
> > Your assertion is that 0^0 can be defined to be
>
> >
>
> > any value and yet have all the usual rules of
>
> >
>
> > exponents apply.
>
>
>
> As I show in Theorem 4, if we avoid base values of 0, we have x^y * x^z = x^(y+z). Likewise for the other Laws of Exponents (Theorems 5 and 7). In practice, this no more onerous a restriction than disallowing zero denominators.
>
>
>
> While we can't use Theorem 4 to prove that 0^2 * 0^3 = 0^(2+3), we can still prove by other means that 0^2 * 0^3 = 1 and 0^(2+3) = 1.
>

Should be 0^2 * 0^3 = 0 and 0^(2+3) = 0

>
>
>
>

> > You've been given examples
>
> >
>
> > that show this is a false statement and have
>
> >
>
> > declined to respond to those examples.
>
> >
>
>
>
> I don't recall any such examples.
>
>
>
>
>

> >
>
>
> >
>
> > rules of exponents specifically exclude using
>
> >
>
> > 0 as a base.
>
>
>
> Yes.
>
>
>

> > Using "logic" like this, you could
>
> >
>
> > define 3^2 to be anything and just word your
>
> >
>
> > theorems "If a is not 3, then these rules work."
>
> >
>
>
>
> Using my definition of ^ of N, if you assume any value for 3^2 other than 9, you will get a contradiction.
>
>
>

> >
>
> >
>
> > So you're asserting that 0^0 can be defined any
>
> >
>
> > way one wants, and it won't matter, _provided that
>
> >
>
> > one doesn't actually look at 0^0.
>
>
>
> [snip rubbish]
>
>
>
> It works because you will still have the same values at every other point. It just formalizes what has been the practice by mathematicians for nearly two centuries -- leaving 0^0 undefined. (Yes, many still cling to 0^0=1.)
>
>
>
> Dan
>
>
> Visit my new math blog at http://www.dcproof.wordpress.com

Date Subject Author
10/16/13 Dan Christensen
10/16/13 Brian Q. Hutchings
11/1/13 ross.finlayson@gmail.com
10/17/13 Robin Chapman
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 fom
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Peter Percival
10/17/13 Dan Christensen
10/17/13 Dan Christensen
11/2/13 Brian Q. Hutchings
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/18/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Ben Bacarisse
10/17/13 Dan Christensen
10/17/13 Robin Chapman
10/17/13 Dan Christensen
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Brian Q. Hutchings
10/17/13 Brian Q. Hutchings
10/18/13 Robin Chapman
10/18/13 Dan Christensen
10/23/13 Shmuel (Seymour J.) Metz
10/25/13 Bart Goddard
10/29/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Robin Chapman
10/30/13 Bart Goddard
10/30/13 Peter Percival
10/30/13 Richard Tobin
10/30/13 fom
10/31/13 David Bernier
10/31/13 David Bernier
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/31/13 Bart Goddard
10/31/13 Dan Christensen
10/31/13 Bart Goddard
10/31/13 Dan Christensen
10/31/13 Bart Goddard
10/30/13 Peter Percival
10/30/13 JT
10/30/13 Dan Christensen
10/30/13 Peter Percival
10/30/13 Dan Christensen
10/30/13 Brian Q. Hutchings
10/30/13 Brian Q. Hutchings
10/30/13 JT
10/30/13 Peter Percival
10/30/13 JT
10/30/13 JT
10/30/13 Brian Q. Hutchings
10/18/13 Robin Chapman
10/18/13 Dan Christensen
10/18/13 fom
10/18/13 Dan Christensen
10/18/13 fom
10/18/13 Dan Christensen
10/18/13 Peter Percival
10/18/13 Dan Christensen
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Michael F. Stemper
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/23/13 Brian Q. Hutchings
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/21/13 Bart Goddard
10/21/13 Dan Christensen
10/21/13 Peter Percival
10/21/13 Bart Goddard
10/21/13 Dan Christensen
10/21/13 Bart Goddard
10/21/13 Peter Percival
10/21/13 fom
10/21/13 Bart Goddard
10/21/13 JT
10/21/13 Dan Christensen
10/21/13 JT
10/21/13 Dan Christensen
10/20/13 Peter Percival
10/20/13 Dan Christensen
10/23/13 Dan Christensen
10/23/13 fom
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 fom
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Brian Q. Hutchings
11/1/13 Dan Christensen
11/1/13 Brian Q. Hutchings
11/2/13 Robin Chapman
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 ross.finlayson@gmail.com
11/3/13 ross.finlayson@gmail.com
11/3/13 Brian Q. Hutchings
11/1/13 Dan Christensen
11/2/13 Bart Goddard
11/2/13 Dan Christensen
11/2/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/13/13 Bart Goddard
11/13/13 Bart Goddard
11/2/13 Virgil
11/2/13 Dan Christensen
11/2/13 Bart Goddard
11/2/13 Paul
11/3/13 Bart Goddard
11/2/13 Dan Christensen
11/2/13 Dan Christensen
11/2/13 Ki Song
11/2/13 Virgil
11/2/13 Michael F. Stemper
11/2/13 Virgil
11/3/13 Michael F. Stemper
11/3/13 Robin Chapman
11/3/13 fom
11/3/13 Jussi Piitulainen
11/3/13 fom
11/4/13 Jussi Piitulainen
11/3/13 JT
11/3/13 JT
11/12/13 Dan Christensen
11/13/13 Dan Christensen