Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:firstname.lastname@example.org:
> As I have said repeatedly, it is assumed to be a natural number, but > no specific value is assigned to it. So, yes, that makes it > "undefined." What is your point, Barty?
The point, as I've said repeatedly, is that your "theorem" assumes that it has a value. If it's not defined, then it has no value (or meaning.) Contradiction. 0^1 is defined in terms of 0^0. So now, 0^1 is undefined. 0^2 is defined in terms of 0^1, so 0^2 is now undefined. Etc. So, by induction, you haven't defined 0^(anything). We, in the business, call this "logic."