Definition:Mapping

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

Let $S\times T$ be their cartesian product.

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 defined as
Some approaches, for example, define a mapping as a many-to-one relation from $S$ to $T$, and then separately specify its requisite left-total nature by restricting $S$ to the domain.

However, this approach is sufficiently different from the mainstream approach that it will not be used on and limited to this mention.

Also see

 * Equivalence of Definitions of Mapping


 * Definition:Linear Transformation
 * Definition:Complex Transformation