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
2x{2}.
See also: Basic Set Theory