Zero to the Power of Zero/Historical Note

Historical Note on Zero to the Power of Zero
Whether $0^0 = 0$ or $0^0 = 1$ has been in question since the concept of zero was first raised as a concept.

From one point of view:
 * $\forall a \in \R: a^0 = 1$

and so $0^0 = 1$.

From the other point of view:
 * $\forall a \in \Z_{\ge 0}: 0^a = 0$

and so $0^0 = 0$.

From the combinatorial perspective, Cardinality of Set of All Mappings would give that $0^0 = 1$, which adds weight to the first of the two possible options.