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:

<math>

\mathcal{A} = \bigcup_{A \in C} A </math>

is a disjoint union if and only if

<math>

\forall A,B \in C \quad st. \ A \ne B: A \cap B = \empty </math>

See also: Basic Set Theory