Definition:Set Intersection/Family of Sets/Universal Set

Definition
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:


 * $\ds \bigcap_{i \mathop \in I} S_i := \set {x \in \mathbb U: \forall i \in I: x \in S_i}$

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


 * $\ds \bigcap_I S_i$

or, if the indexing set is clear from context:


 * $\ds \bigcap_i S_i$

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