Definition:Set of All Mappings

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

The set of (all) mappings from $S$ to $T$ is:


 * $T^S := \left\{{f \subseteq S \times T: f: S \to T \text{ is a mapping}}\right\}$

Also known as
It is sometimes unwieldy to write $T^S$, particularly when $T$ and/or $S$ have themselves superscripts or subscripts attached.

In these cases, it is convenient to write $\left[{S \to T}\right]$ for the set of mappings from $S$ to $T$.

Also see

 * Cardinality of Set of All Mappings