Editing Set (mathematics) (section)

===Intersection===
[[File:Venn0001.svg|thumb|<div class="center">The ''intersection'' of {{mvar|A}} and {{mvar|B}}, denoted {{math|''A'' ∩ ''B''}}</div>]]
The ''[[set intersection|intersection]]'' of two sets {{tmath|A}} and {{tmath|B}} is a set denoted {{tmath|A \cap B}} whose elements are those elements that belong to both {{tmath|A}} and {{tmath|B}}. That is,
<math display=block>A \cap B=\{x\mid x\in A \land x\in B\},</math>
where {{tmath|\land}} denotes the [[logical and]]. 

Intersection is [[associative]] and [[commutative]]; this means that for proceeding a sequence of intersections, one may proceed in any order, without the need of parentheses for specifying the [[order of operations]]. Intersection has no general [[identity element]]. However, if one restricts intersection to the subsets of a given set {{tmath|U}}, intersection has {{tmath|U}} as identity element.

If {{tmath|\mathcal S}} is a nonempty set of sets, its intersection, denoted 
<math display=inline>\bigcap_{A\in \mathcal S} A,</math> 
is the set whose elements are those elements that belong to all sets in {{tmath|\mathcal S}}. That is,
<math display=block>\bigcap_{A\in \mathcal S} A =\{x\mid (\forall A\in \mathcal S)\; x\in A\}.</math>

These two definitions of the intersection coincide when {{tmath|\mathcal S}} has two elements.