Cardinality of Set of Self-Mappings on Finite Set

Theorem
Let $S$ be a finite set.

Let the cardinality of $S$ be $n$.

The cardinality of the set of all mappings from $S$ to itself (that is, the total number of self-maps on $S$) is:


 * $\card {S^S} = n^n$

Proof
This is a specific example of Cardinality of Set of All Mappings where $S = T$.