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Topic: Formal proof of the ambiguity of 0^0
Replies: 6   Last Post: Nov 17, 2013 5:05 PM

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 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: Formal proof of the ambiguity of 0^0
Posted: Nov 17, 2013 3:13 PM

On Sunday, November 17, 2013 2:55:58 PM UTC-5, Julio Di Egidio wrote:
> "Dan Christensen" <Dan_Christensen@sympatico.ca> wrote in message
>
>

> > On Sunday, November 17, 2013 2:04:57 PM UTC-5, Julio Di Egidio wrote:
>
> <snip>
>
>
>

> >> Yes, but you still do not address any objections to that position.
>
> >> Namely,
>
> >> that you have *not* proved that 0^0 *must* be undefined,
>
> >
>
> > You can't formally "prove" such an informal statement; you can only
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> > provide a rationale as I have done.
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>
>
> That is what *I* would say, while you keep proposing "formal proofs" just at
>
> the next paragraph!
>

I have provided a rationale for leaving 0^0 undefined, one based only formal proofs. No hand-waving, no analogies to various combinatorial or set-theoretic notions. Just ordinary, natural-number arithmetic, as you would expect for a definition of repeated multiplication on N.

>
>

> >> you have rather at
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> >> best provided some formal support to the naive high-school level approach
>
> >> that simply leaves it undefined. Big difference.
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> >
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> > I have formally proven that for all x0 in N (including 0), there exists an
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> > exponent-like functions ^ such that:
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>
>
> Such that "any number works": exactly what I had explained.
>

That's pretty much what we mean by 0^0 being undefined.

Dan