\begin{definition}[Definition:Set Intersection/Family of Sets/Universal Set]
Let $\mathbb U$ be a universal set.
Let $I$ be an indexing set.
Let $\family {S_i}_{i \mathop \in I}$ be an indexed family of subsets of $\mathbb U$.
Then the '''intersection''' of $\family {S_i}$ is defined and denoted as:
:$\ds \bigcap_{i \mathop \in I} S_i := \set {x \in \mathbb U: \forall i \in I: x \in S_i}$
\end{definition}