# Disjoint union

In

set theory, a

**disjoint union** is a type of union (

Set theoretic union), in which each element of the union is disjoint from the others: intersection with every other element of the union is the

empty set.

i.e. Suppose C is a collection of sets, then:

is a disjoint union

if and only if

To take the disjoint union of sets that are not in fact disjoint, one can use an indexing device. For example given A

_{1} and A

_{2}, which may have common elements, with union B, the disjoint union as a subset of B x {1,2} is the union of A

_{1} x {1} and A

_{2}x{2}.

See also: Basic Set Theory