Definition:Image (Relation Theory)/Relation/Relation

Definition
Let $\mathcal R \subseteq S \times T$ be a relation.

The image (or image set) of $\mathcal R$ is the set:


 * $\operatorname{Im} \left ({\mathcal R}\right) = \mathcal R \left ({S}\right) = \left\{ {t \in T: \exists s \in S: \left({s, t}\right) \in \mathcal R}\right\}$

Also see

 * Definition:Mapping, in which the context of an image is usually encountered.


 * Definition:Domain of Relation
 * Definition:Codomain of Relation
 * Definition:Range


 * Definition:Preimage of Relation (also known as Definition:Inverse Image)