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.
Contents |
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.
The codomain of a mapping $f: S \to T$ is the set $T$.
It can be denoted $\operatorname{Cdm} \left({f}\right)$.
Some sources, for example T.S. Blyth: Set Theory and Abstract Algebra (1975), also refer to the codomain as the arrival set.
