Definition 4

Let $\mathfrak{a}$ and $\mathfrak{b}$ be cardinals. The cardinal of the set of mappings of $\mathfrak{b}$ into $\mathfrak{a}$ is denoted by $\mathfrak{a}^{\mathfrak{b}}$, by abuse of notation.

The abuse of notation here lies in the the fact that $\mathfrak{a}^{\mathfrak{b}}$ already denotes the set of graphs of mappings of $\mathfrak{b}$ into $\mathfrak{a}$ (Chapter II, § 5, no. 3), and this set is not necessarily a cardinal (Exercise 2). It will always be clear from the context which meaning is to be attached to the symbol $\mathfrak{a}^{\mathfrak{b}}$.