Definition:Composition of Mappings/Warning

Definition
Let $f_1: S_1 \to S_2$ and $f_2: S_2 \to S_3$ be mappings such that the domain of $f_2$ is the same set as the codomain of $f_1$.

If $\Dom {f_2} \ne \Cdm {f_1}$, then the composite mapping $f_2 \circ f_1$ is not defined.

This definition is directly analogous to that of composition of relations owing to the fact that a mapping is a special kind of relation.