\begin{definition}[Definition:Indexing Set/Family of Sets]
Let $\SS$ be a set of sets.
Let $I$ be an indexing set.
Let $\family {S_i}_{i \mathop \in I}$ be a family of elements of $\SS$ indexed by $I$.
Then $\family {S_i}_{i \mathop \in I}$ is referred to as an '''indexed family of sets'''.
\end{definition}