# Definition:Codomain of Mapping/Terminology

## Codomain of Mapping: a note on Terminology

Some sources refer to the codomain of a mapping as its range.

However, other sources equate the term range with the image set.

Other sources brush the question aside by refraining from giving the codomain a name at all.

For example, from 1975: W.A. Sutherland: *Introduction to Metric and Topological Spaces*: Notation and Terminology:

*A map or function (the terms are used interchangeably) between sets $A, B$ is written $f: A \to B$. We call $A$ the domain of $f$, and we avoid calling $B$ anything.*

As there exists significant ambiguity as to whether the range is to mean the codomain or image set, it is advised that the term range is not used.

The notation $\Cdm f$ has not actually been found by this author anywhere in the literature. In fact, except in the field of category theory, no symbol for the concept of codomain *has* been found, despite extensive searching.

However, using $\Cdm f$ to mean **codomain** is a useful enough shorthand to be worth coining.

This is the approach which has been taken on this website.