Definition:Set Intersection/Countable Intersection

Definition
Let $\Bbb S = \left\{{S_0, S_1, S_2, \ldots}\right\}$ be a set of a countably infinite number of sets.

Then:


 * $\displaystyle \bigcap \Bbb S := \bigcap_{i \mathop \in \N} S_i = \left\{{x: \forall i \in \N: x \in S_i}\right\}$

This can also be denoted:
 * $\displaystyle \bigcap_{i \mathop = 1}^\infty S_i$

but its usage is strongly discouraged.

If it is clear from the context that $i \in \N$, we can also write $\displaystyle \bigcap_{\N} S_i$.