# Definition:Image of Relation/Also known as

## Definition

The **image** of a relation $\RR$, when in the context of set theory, is often seen referred to as the **image set** of $\RR$.

Some sources refer to this as the **direct image** of a relation, in order to differentiate it from an **inverse image**.

Rather than apply a relation $\RR$ directly to a subset $A$, those sources often prefer to define the direct image mapping of $\RR$ as a separate concept in its own right.

Other sources call the **image** of $\RR$ its **range**, but this convention is discouraged because of potential confusion.

Many sources denote the **image** of a relation $\RR$ by $\map {\operatorname {Im} } \RR$, but this notation can be confused with the imaginary part of a complex number $\map \Im z$.

Hence on $\mathsf{Pr} \infty \mathsf{fWiki}$ it is preferred that $\Img \RR$ be used.