Definition:Codomain (Relation Theory)/Relation

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

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

A note on terminology
Some sources refer to the codomain of a relation as its range.

However, other sources equate the term range with the image set.

As there exists significant ambiguity as to whether the range is to mean the codomain or image set, it is advised that the term range is not used.

The notation $\operatorname{Cdm} \left({\mathcal R}\right)$ has not actually been found by this author anywhere in the literature. In fact, outside the field of category theory, no symbol for the concept of codomain has been found, despite extensive searching.

However, using $\operatorname{Cdm}$ to mean codomain is a useful enough shorthand to be worth coining. That is the approach which has been taken on this website.

Also see

 * Domain
 * Range


 * Image
 * Preimage