# Cardinality of Set of All Mappings/Infinite Sets

Let $S$ and $T$ be sets such that either $S$ or $T$ is infinite.
The cardinality of the set of all mappings from $S$ to $T$ (that is, the total number of mappings from $S$ to $T$) is:
$\card {T^S} = \card T^{\card S}$