Operations on sets | Basic concepts in set theory
Disjoint union
In mathematics, a disjoint union (or discriminated union) of a family of sets is a set often denoted by with an injection of each into such that the images of these injections form a partition of (that is, each element of belongs to exactly one of these images). A disjoint union of a family of pairwise disjoint sets is their union. In category theory, the disjoint union is the coproduct of the category of sets, and thus defined up to a bijection. In this context, the notation is often used. The disjoint union of two sets and is written with infix notation as . Some authors use the alternative notation or (along with the corresponding or ). A standard way for building the disjoint union is to define as the set of ordered pairs such that and the injection as (Wikipedia).
