Definition:Indexing Set

Definition
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.