> Well, at least you now seem to have come around to the fact that 0^0 > is ambiguous with two, if not infinitely many possibilities (which > there are). But even with only two possibilities, you would still > have to stipulate limits on the definition of 0 exponents. In a > proof, you still wouldn't be able to refer to the value 0^0 because > it isn't specified in the definition and it doesn't seem you can > infer it.
Dan's definition of ^ doesn't allow the value of 0^0 to be inferred. That is a big hint that the definition is inadequate.
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg