Disjoint union
In set theory, a disjoint union is a type of 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
