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