Disjoint union
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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 A₁ and A₂, which may have common elements, with union B, the disjoint union as a subset of B x {1,2} is the union of A₁ x {1} and A₂x{2}.

See also: Basic Set Theory

The original article can be found at: http://en.wikipedia.org/wiki/Disjoint_union.
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