Definition:Indexing Set/Term

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 value of $x$ at an index $i$ is called 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.