[math-fun] Proof that 0^0 = 1

I hear 0^0 should be defined as 1 for convenience, but perhaps there are proofs this has to be so (the *value* zero raised to the *value* 0, not the indeterminate limits of the form 0^0). What's your favorite proof that 0^0 = 1? Here's one. 0^0 = (1 - 1)^0 = \sum_{k=0}^0 \binom{0}{k} 1^{0-k} (-1)^k = \binom{0}{0} * 1 * 1 = \frac{0!}{0! \cdot 0!} * 1 = 1 * 1 = 1 Andres.