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:


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

Also denoted as
The set $\displaystyle \bigcap_{i \mathop \in I} X_i$ can also be seen denoted as:


 * $\displaystyle \bigcap_I X_i$

or, if the indexing set is clear from context:


 * $\displaystyle \bigcap_i X_i$

However, on this website it is recommended that the full form is used.