Definition:Indexing Set/Indexed Set

Definition
Let $I$ and $S$ be sets.

Let $x: I \to S$ be a mapping.

Let the domain $I$ of $x$ be the indexing set of the indexed family $\left \langle {x_i} \right \rangle_{i \mathop \in I}$.

The image $x \left[{I}\right]$ of $x$ is called an indexed set.