# Definition:Codomain (Set Theory)

Jump to navigation
Jump to search

*This page is about Codomain in the context of Set Theory. For other uses, see Codomain.*

## Definition

### Relation

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

It can be denoted $\Cdm {\mathcal R}$.

### 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**.