Definition:Set Intersection/Family of Sets

Definition
Let $I$ be an indexing set.

Let $\left \langle {X_i} \right \rangle_{i \mathop \in I}$ be a family of subsets of a set $S$.

Then the intersection of $\left \langle {X_i} \right \rangle$ is defined as:


 * $\displaystyle \bigcap_{i \mathop \in I} X_i = \left\{{y: \forall i \in I: y \in X_i}\right\}$

This notation can also be used as $\displaystyle \bigcap_i X_i$ to be written $\displaystyle \bigcap_{i \mathop \in I} X_i$.