Definition:Composition of Mappings/Definition 1

Definition
Let $S_1$, $S_2$ and $S_3$ be sets.

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 $f_1$.

The composite mapping $f_2 \circ f_1$ is defined as:


 * $\forall x \in S_1: \map {\paren {f_2 \circ f_1} } x := \map {f_2} {\map {f_1} x}$


 * CompositeMapping.png

Also see

 * Equivalence of Definitions of Composition of Mappings