Definition:Indexing Set

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

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

Let $x_i$ denote the image of an element $i \in I$ of the domain $I$ of $x$.

Let $\family {x_i}_{i \mathop \in I}$ denote the set of the images of all the elements $i \in I$ under $x$.

When a mapping is used in this context, the domain $I$ of $x$ is called the indexing set of the terms $\family {x_i}_{i \mathop \in I}$.

Also known as
Some authors use the term index set for indexing set, while others uses set of indices.

Also see
Compare the definition of a sequence, where the indexing set used is the set of natural numbers $\N$, or a subset of $\N$.