0^0 = 1?

[AlexFekken]

I just realise that I may have caused some confusion with the words 'the unique "limit" (in some sense)' in my original post. This wasn't to imply that I was going to consider alternative definitions of what it means to be a "limit", but rather to cover the case of dealing with integer values only for y (the only case for which setting 0^0 to 1 seems justified).

When y only takes on integer values then the idea of taking a limit where y is going to 0 may seem strange, but "in some sense" (the discrete topology on the integers) taking this limit follows the standard mathematical definition and is consistent with other "limits". It basically amounts to setting y to 0 and taking the usual limit for x only (i.e. it becomes 1-dimensional again).