Definition:Mapping

Definition
Let $S$ and $T$ be sets.

Domain, Codomain, Image, Preimage
As a mapping is also a relation, all the results and definitions concerning relations also apply to mappings.

In particular, the concepts of domain and codomain carry over completely, as do the concepts of image and preimage.

Mapping as Unary Operation
It can be noted that a mapping can be considered as a unary operation.

Also known as
Words which mean the same thing as mapping include:
 * map
 * transformation (particularly in the context of self-maps)
 * operator
 * function (usually in the context of numbers)

Sources defining a mapping (function) to be only a many-to-one relation refer to a mapping (function) as a total mapping (total function).

The wording can vary.

A mapping $f$ from $S$ to $T$ is also described as a mapping on $S$ into $T$.

Also see

 * Definition:Linear Transformation
 * Definition:Complex Transformation