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: