Definition:Image (Relation Theory)/Mapping

Definition
The image (or image set) of a mapping $f: S \to T$ is the set:


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

Image of an Element
Let $f: S \to T$ be a mapping.

Let $s \in S$.

The image of $s$ by $f$ is defined as:


 * $\operatorname{Im} \left ({s}\right) = f \left ({s}\right) = \left\{ {t \in T: \left({s, t}\right) \in f}\right\}$

That is, $f \left ({s}\right)$ is the element of the codomain of $f$ related to $s$ by $f$.

Also see

 * Domain
 * Codomain
 * Range


 * Preimage (also known as inverse image)