# Definition:Codomain (Set Theory)

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*This page is about the concept of codomain in set theory. For other uses, see Definition:Codomain.*

## Definition

### Relation

The **codomain** of a relation $\mathcal R \subseteq S \times T$ is the set $T$.

It can be denoted $\operatorname{Cdm} \left({\mathcal R}\right)$.

### Mapping

The term **codomain** is usually seen when the relation in question is actually a mapping:

Let $f: S \to T$ be a mapping.

The **codomain** of $f$ is the set $T$.

It is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ by $\Cdm f$.

## Also known as

Some sources write **codomain** as **co-domain**.