Intersection of sets

One of the basic operations on sets. Suppose one has a finite or infinite collection of sets $\{A_{\alpha }\}$ (the subscript $\alpha$ serves to distinguish the elements of the given collection). Then the set of those elements that are contained in all these sets (the set of elements common to all $A_{\alpha }$) is called the intersection of these sets.

The intersection of these sets is denoted by $\bigcap A_{\alpha }$.