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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 UTC5, Julio Di Egidio wrote: > "Dan Christensen" <Dan_Christensen@sympatico.ca> wrote in message > > news:668d009ce06b4e3c857186a92e5375c5@googlegroups.com... > > > On Sunday, November 17, 2013 2:04:57 PM UTC5, 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 > > > provide a rationale as I have done. > > > > 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 handwaving, no analogies to various combinatorial or settheoretic notions. Just ordinary, naturalnumber arithmetic, as you would expect for a definition of repeated multiplication on N.
> > > >> you have rather at > > >> best provided some formal support to the naive highschool level approach > > >> that simply leaves it undefined. Big difference. > > > > > > I have formally proven that for all x0 in N (including 0), there exists an > > > exponentlike functions ^ such that: > > > > Such that "any number works": exactly what I had explained. >
That's pretty much what we mean by 0^0 being undefined.
Dan Download my DC Proof 2.0 software at http://www.dcproof.com Visit my new math blog at http://www.dcproof.wordpress.com



