Definition:Image (Relation Theory)/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

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


 * Domain
 * Codomain
 * Range


 * Preimage (also known as inverse image)