Exactly. And that, as well, is the reason why a^0=1 for every non-zero real number a: because you NEED to divide by a, in the proof for real numbers' Calculus.
On set theory, 0^0 it's the number of functions from Ø (the empty set) on itself; wich, whatever wiki says (in this case), it's also undefined. It could be 1 indeed, if you take the one and only empty function identical to Ø, because Ø is a subset of each and every set (wich includes the set equal to the class of functions of any set); but it could also be infinite (or "indetermined"), since you cannot proove ANY relation between ANY sets NOT being a function on and from Ø, without coming to a contradiction with Ø's emptiness; that is: any random relation MUST be a function from Ø on Ø, because you cannot show any especific element from Ø intersected with domain of the relation -wich are none- that is NOT related with one and only one element at the -equally empty- image; in other words: it IS a function, simply because you cannot show the element that would disprove it as such. That sort of proof, on wich you do not show the propper deduction, but argument instead the inexistence of a case that contradicts your (universal) proposition, it's called Vacuous Truth ( http://en.wikipedia.org/wiki/Vacuous_truth )...
Neddles to say, this whole affair is very counter-intuitive. As said, it depends on the fact that we aknowledge that exponentiation on real numbers does NOT mean the same than in natural numbers (multipliying several times, wich is -allegedly- merely adding several times), but something entirely new. However, if we decide to go with the convention of 0^0=1, under some alleged convenience, this would still makes us face a serious ontological question:
How is it possible that starting with nothing and operating with it, 0 times, suddenly gives us something?...
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