Definition:Indexing Set/Term

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 $x$.

The image of $x$ at an index $i$ is referred to as a term of the (indexed) family, and is denoted $x_i$.

Also known as
A term of a family is also known as an element of that family.