**Definition 2**. Let \(A\) and \(B\) be sets. A **map** is a set
\(\varphi \subseteq\) \(A \times B\) such that for each \(a \in A\)
there is exactly one \(b \in B\) with \(\left( a, b \right) \in \varphi\).

**Definition 2**. Let \(A\) and \(B\) be sets. A **map** is a set
\(\varphi \subseteq\) \(A \times B\) such that for each \(a \in A\)
there is exactly one \(b \in B\) with \(\left( a, b \right) \in \varphi\).