Editing Set (mathematics) (section)

===Union===
[[File:Venn0111.svg|thumb|<div class="center">The ''union'' of {{math|''A''}} and {{math|''B''}}, denoted {{math|''A'' ∪ ''B''}}</div>]]
The ''[[set union|union]]'' of two sets {{tmath|A}} and {{tmath|B}} is a set denoted {{tmath|A \cup B}} whose elements are those elements that belong to {{tmath|A}} or {{tmath|B}} or both. That is,
<math display=block>A \cup B=\{x\mid x\in A \lor x\in B\},</math>
where {{tmath|\lor}} denotes the [[logical or]]. 

Union 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]]. The empty set is an [[identity element]] for the union operation.

If {{tmath|\mathcal S}} is a  set of sets, its union, denoted 
<math display=inline>\bigcup_{A\in \mathcal S} A,</math> 
is the set whose elements are those elements that belong to at least one set in {{tmath|\mathcal S}}. That is,
<math display=block>\bigcup_{A\in \mathcal S} A =\{x\mid (\exists A\in \mathcal S)\; x\in A\}.</math>

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