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: The ambiguity of 0^0 on N
Replies: 106   Last Post: Sep 29, 2013 10:06 AM

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: The ambiguity of 0^0 on N
Posted: Sep 19, 2013 10:32 AM

On Thursday, September 19, 2013 7:14:11 AM UTC-4, Peter Percival wrote:
> Dan Christensen wrote:
>

> > On Wednesday, September 18, 2013 8:33:15 PM UTC-4, Rotwang wrote:
>
> >
>
> >>
>
> >> The problem is that Dan has things backwards; rather than picking
>
> >> a
>
> >>
>
> >> definition and determining what properties it satisfies, he's
>
> >> picked a
>
> >>
>
> >> few properties satisfied by the usual definition, noticed that
>
> >> those
>
> >>
>
> >> properties aren't sufficient to derive the usual definition, and is
>
> >> now
>
> >>
>
> >> insisting that we should therefore abandon the usual definition
>
> >> unless
>
> >>
>
> >> someone can show that the other possible definition that satisfies
>
> >> those
>
> >>
>
> >> properties gives rise to a contradiction. This makes no sense.
>
> >
>
> > Some elements of what you call the "usual definition" are redundant.
>
>
>
> The usual definition only has two elements:
>
>
>
> x^0 = 1
>
> x^{y+1} = x x^y
>
>
>
> and *some* of those are redundant, are they?
>

I have shown that we need only explicitly define ^ in N for exponents of 2 or more. Apart from the base of 0, we can derive values for exponents 0 and 1. In that sense, the usual definition has redundant elements.

>
>
>
>

> > They can actually be derived from other elements. (See my proof.)
>
> >
>
> > Another element of your "usual definition" -- your 0^0=1 -- may even
>
>
>
>
> May? Prove that it *does* and people will sit up and take notice.
>

You have it backwards. The burden of proof lies with the advocates of proving that 0^0 should be assigned any particular value. I am not opposed to doing so, but I want some rigorous proof before making decisions based on that value.

>
>

> > I guess that's why they leave it out in
>
> > other "usual definitions."
>
>
>
> They? Who?
>

Many standard textbooks leave 0^0 undefined. This is not the realm of cranks or radicals. On the contrary, it is the most conservative option.

Dan

Date Subject Author
9/18/13 Dan Christensen
9/18/13 Peter Percival
9/18/13 Dan Christensen
9/18/13 Peter Percival
9/18/13 Virgil
9/18/13 Dan Christensen
9/18/13 Rotwang
9/18/13 Rock Brentwood
9/18/13 Rotwang
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/20/13 fom
9/19/13 Virgil
9/19/13 Virgil
9/19/13 Rotwang
9/18/13 Virgil
9/18/13 fom
9/18/13 Rotwang
9/28/13 Shmuel (Seymour J.) Metz
9/29/13 Marshall
9/19/13 Dan Christensen
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Michael F. Stemper
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Dan Christensen
9/20/13 fom
9/20/13 Dan Christensen
9/20/13 fom
9/19/13 fom
9/19/13 fom
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 Rotwang
9/19/13 Dan Christensen
9/19/13 Helmut Richter
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 fom
9/19/13 fom
9/19/13 JT
9/19/13 JT
9/19/13 Michael F. Stemper
9/19/13 JT
9/19/13 JT
9/19/13 JT
9/19/13 Helmut Richter
9/28/13 Shmuel (Seymour J.) Metz
9/19/13 fom
9/19/13 Peter Percival
9/19/13 Dan Christensen
9/19/13 Peter Percival
9/19/13 Karl-Olav Nyberg
9/19/13 fom
9/19/13 fom
9/19/13 Rotwang
9/19/13 Dan Christensen
9/19/13 fom
9/25/13 Rotwang
9/26/13 Dan Christensen
9/27/13 Brian Q. Hutchings
9/19/13 fom
9/18/13 Rock Brentwood
9/19/13 Dan Christensen
9/19/13 Dan Christensen
9/19/13 Rotwang
9/19/13 Dan Christensen
9/19/13 fom
9/20/13 Dan Christensen
9/20/13 fom
9/20/13 Dan Christensen
9/20/13 Peter Percival
9/20/13 Peter Percival
9/20/13 Dan Christensen
9/20/13 Virgil
9/20/13 Peter Percival
9/20/13 fom
9/20/13 Michael F. Stemper
9/20/13 LudovicoVan
9/21/13 Michael F. Stemper
9/21/13 LudovicoVan
9/21/13 Richard Tobin
9/20/13 Peter Percival
9/20/13 Peter Percival
9/21/13 Dan Christensen
9/19/13 Karl-Olav Nyberg