4.2 Surjection

A function is a surjection iff $\forall f \in Y: \exists e \in X: (e, f) \in L$ . Surjection is also called ``onto''.

In English, this means that every value in $Y$ has something in $X$ to map to it. Let us consider $L = \{(x,y)\vert x \in \mathbb{I}, y \in \{0, 1, \ldots 4\}, y = x \mod 5\}$ . In this case, even though $L$ is not an injection because $(0, 0), (5, 0) \in L$ , it is a surjection.