Definition:Composition of Mappings/General Definition

Definition
Let $f_1: S_1 \to S_2, f_2: S_2 \to S_3, \ldots, f_n: S_n \to S_{n + 1}$ be mappings such that the domain of $f_k$ is the same set as the codomain of $f_{k - 1}$.

Then the composite of $f_1, f_2, \ldots, f_n$ is defined and denoted as:


 * $\forall x \in S_1: \left({f_n \circ \cdots \circ f_2 \circ f_1}\right) \left({x}\right) := f_n \left({\ldots{} f_2 \left({f_1 \left({x}\right)}\right)\ldots}\right)$