Definition:Range of Relation

Relation
The range of a relation $$\mathcal{R} \subseteq S \times T$$ is the set $$T$$ and is denoted $$\operatorname {Rng} \left({\mathcal{R}}\right)$$ or $$\operatorname {Ran} \left({\mathcal{R}}\right)$$.

Some authors use the term codomain instead of range.

Some sources, for example, define the range as:
 * $$\operatorname{Rng} \left({\mathcal{R}}\right) = \left\{{t \in T: \exists s \in S: \left({s, t}\right) \in \mathcal{R}}\right\}$$

... that is, the same as what we call the image.

What we call the range is, in this context, called the codomain.

So it is wise to be careful to make sure exactly what is meant in the context it appears.

Mapping
The term range (or codomain) is usually seen when the relation in question is actually a mapping.

Some sources, for example, call the codomain the arrival set.

Also see

 * Domain
 * Image


 * Preimage