```Date: Oct 30, 2013 5:15 PM
Author: Bart Goddard
Subject: Re: Formal proof of the ambiguity of 0^0

Dan Christensen <Dan_Christensen@sympatico.ca> wrote innews:8c1d6b6d-986e-4fd5-b7ec-3b1236964c2c@googlegroups.com: >> You're claiming to extend exponentiation to N_0, but>> >> all of your rules say "nonzero base."> > [snip]> > Nothing wrong with that.In mathematics, contradiction is the ONLY sort of wrongthere is.  And you're definitely contradicting yourself.You're extending without extending.> Mathematicians have being doing this> implicitly for nearly two centuries. Now, it has a rigorous> foundation. No, they have not. I'm trying to imagine a mathematician"extending" real number multiplicationto the complex numbers, but declaring, in all partsof his definition, that it doesn't apply to non-realnumbers. And, as if that wasn't bizarrely stupid enough, to follow up with "therefore it doesn't matterhow you define complex multiplication...."> 0^0 is an unspecified natural number. If it's not specified, then it's not defined.If it's not defined, there is no extention.  > Again, my definition refers specifically to 0-exponents, and I have> referred here to a theorem concerning 0-bases that can be derived from> that definition. Sure sounds like "extending" to me. But you've shown yourself to be a particularly badjudge of what an extention is, so that fact that itsounds like it "to you" means nothing.  (And, in fact,actually argues against.)  You can't claim an extentionto N_0, unless 0^0 is defined.
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