\begin{definition}[Definition:Indexing Set/Term]
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 $x_i$.
\end{definition}