Definition:Set Intersection/Finite Intersection

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

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

where $\N^*_n = \left\{{1, 2, 3, \ldots, n}\right\}$.

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

Other notations for this concept are:
 * $\displaystyle \bigcap_{i \mathop = 1}^n S_i$
 * $\displaystyle \bigcap_{1 \mathop \le i \mathop \le n} S_i$