TITLE: Name for the set of possible functions $A\to B$
QUESTION [10 upvotes]: Everybody knows the Cartesian product $A \times B$, where $|A\times B| = |A| \cdot |B|$.
But is there a name for the set of possible functions $A \to B$, where $|A \to B| = |B|^{|A|}$
E.g. 
$$
A = \{0, 1\} \\
f_1,f_2,f_3,f_4\colon A \to A \\
f_1\colon x \mapsto 0 \\
f_2\colon x \mapsto 1 \\
f_3\colon x \mapsto x \\
f_4\colon 0 \mapsto 1 \\
f_4\colon 1 \mapsto 0 \\
$$
I know of the symmetric group, which is a similiar notion, but it only covers bijections, and not all possible functions.

REPLY [12 votes]: $B^A$ is common in mathematics.
Computer scientists (or at least the undersigned computer scientist) will sometimes prefer to cut the notational crap and declare "$A\to B$" to be the name of the set of maps from $A$ to $B$.