Definition:Indexing Set/Index

This page is about index in the context of indexing sets. For other uses, see index.

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 element $i \in I$ under $x$.

An element of the domain $I$ of $x$ is called an index.

The plural of index is indices.

Compare vertex and apex, which have a similar plural form.