Definition:Set Intersection/Set of Sets

Definition
Let $\Bbb S$ be a set of sets

The intersection of $\Bbb S$ is:
 * $\displaystyle \bigcap \Bbb S := \left\{{x: \forall S \in \Bbb S: x \in S}\right\}$

That is, the set of all objects that are elements of all the elements of $\Bbb S$.

Thus:
 * $\displaystyle \bigcap \left\{{S, T}\right\} := S \cap T$

Also denoted as
Some sources denote $\displaystyle \bigcap \mathbb S$ as $\displaystyle \bigcap_{S \in \mathbb S} S$.