Definition:Indexing Set

Let $$f: A \to S$$ be a mapping.

Let some symbol be chosen, say $$x$$. Then $$f \left({\alpha}\right)$$ is denoted $$x_\alpha$$ for all $$\alpha \in A$$, and $$f$$ itself is denoted $$\left \langle {x_\alpha} \right \rangle_{\alpha \in A}$$.

In this situation, the domain $$A$$ of $$f$$ is called the indexing set of $$\left \langle {x_\alpha} \right \rangle_{\alpha \in A}$$.

In this context,$$\left \langle {x_\alpha} \right \rangle_{\alpha \in A}$$ is called a family of elements of $$S$$ indexed by $$A$$ instead of as a "mapping from $$A$$ to $$S$$", or just an indexed family.