Date: Oct 23, 2013 12:55 PM
Author: Dan Christensen
Subject: Re: Formal proof of the ambiguity of 0^0

As some have suggested here, context may have a bearing on this matter, but care should be taken so as not confuse the subtly different concepts. 

We could have two different functions: what might be called multiplicative exponentiation (x^y, the usual kind), and what might be called combinatorial exponentiation (f where f(x,y) = 1 if x=y=0, = x^y otherwise). Perhaps a different notation should be used for each where it matters, e.g. in formal, foundational proofs.

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