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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: The ambiguity of 0^0 on N
Posted: Sep 19, 2013 7:13 PM
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In article <l1ema5\$tj5\$1@news.albasani.net>,
Peter Percival <peterxpercival@hotmail.com> 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?

The first of those two "elements" is sometimes specifically limited to
instances where x =/= 0.
>
>

> > They can actually be derived from other elements. (See my proof.)
> >
> > Another element of your "usual definition" -- your 0^0=1 -- may even
> > lead to a contradiction.

>
> May? Prove that it *does* and people will sit up and take notice.
>

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

>
> They? Who?

--

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

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