\begin{definition}[Definition:Disjoint Sets/Family]
Let $I$ be an indexing set.
Let $\family {S_i}_{i \mathop \in I}$ be a family of sets indexed by $I$.
Then $\family {S_i}_{i \mathop \in I}$ is '''disjoint''' {{iff}} their intersection is empty:
:$\ds \bigcap_{i \mathop \in I} S_i = \O$
\end{definition}