Definition:Set Intersection/Countable Intersection

Definition
Let $S = S_1 \cap S_2 \cap \ldots \cap S_n$. Then:


 * $\displaystyle \bigcap_{i \mathop \in \N^*_n} S_i = \left\{{x: \forall i \in \N^*_n: x \in S_i}\right\}$

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

An alternative notation for the same concept is $\displaystyle \bigcap_{i \mathop = 1}^n S_i$.