Definition:Disjoint Union (Set Theory)/Notation

Notation for Disjoint Union (Set Theory)

The notations:

$\ds \sum_{i \mathop \in I} S_i$ and $\ds \coprod_{i \mathop \in I} S_i$

can also be seen for the disjoint union of a family of sets.

When two sets are under consideration, the notation:

$A \sqcup B$

or:

$A \coprod B$

are usually used.

Some sources use:

$A \vee B$

The notations:

$A + B$

or

$A \oplus B$

are also encountered sometimes.

This notation reflects the fact that, from the corollary to Cardinality of Set Union, the cardinality of the disjoint union is the sum of the cardinalities of the terms in the family.

It is motivated by the notation for a coproduct in category theory, combined with Disjoint Union is Coproduct in Category of Sets.

Compare this to the notation for the cartesian product of a family of sets.