Cardinality of Set of All Mappings/Examples/Set of Cardinality 4

Example of Cardinality of Set of All Mappings
Let $S$ be a set whose cardinality is $4$:


 * $\card S = 4$

Then there are $256$ mappings from $S$ to itself.

Proof
Let $T$ be the set of mappings from $S$ to itself.

From Cardinality of Set of All Mappings:
 * $\card T = \card S^\card S = 4^4 = 256$

The result follows by Examples of Factorials.