# Definition:Codomain (Set Theory)

## 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.