Cardinality of Set of All Mappings

Theorem
Let $S$ and $T$ be sets.

The cardinality of the set of all mappings from $S$ to $T$ (that is, the total number of mappings from $S$ to $T$) is:


 * $\left|{T^S}\right| = \left|{T}\right| ^ {\left|{S}\right|}$

Comment
The question of whether to define $0^0 = 0$ or $0^0 = 1$ keeps students awake arguing for hours.

Here's another argument, in case you're not convinced, for defining $0^0 = 1$ as opposed to $0^0 = 0$ - another result kept nice and neat.