A MappinG is simply a “rule” that assigns to each member of a Set A, a unique element of a set B. 
A MappinG is simply a "rule" that assigns to each member of a SeT A, a unique element of a SeT B. 
There are nonmathematical MappinGs?. Consider the “rule,” WGT that assigns to every living human being in United States their weight in pounds. Then the set A = {people living in the United States} and B = {x: 0<x<=1000}. For example: 
There are nonmathematical MappinGs. Consider the “rule,” WGT that assigns to every living human being in United States their weight in pounds. Then the set A = {people living in the United States} and B = {x: 0<x<=1000}. For example: 
There are mathematical MappinGs? as well. Consider the “rule,” ABS that assigns to each integer, its absolute value. Let set C = I, and the set D = I, also. Then, for example: 
There are mathematical MappinGs as well. Consider the “rule,” ABS that assigns to each integer, its absolute value. Let set C = I, and the set D = I, also. Then, for example: 
There are 4 basic kinds of MappinGs?. 
There are 4 basic kinds of MappinGs. 

In terms of formal SetTheory, a Mapping from X to Y is usually defined as a MathematicalRelation where each x in X is related to one, and only one, element of Y. This element is the image of x. However, there are lots of other equivalent definitions. 
There are nonmathematical MappinGs. Consider the “rule,” WGT that assigns to every living human being in United States their weight in pounds. Then the set A = {people living in the United States} and B = {x: 0<x<=1000}. For example:
There are 4 basic kinds of MappinGs.
1) into MappinG: this is a MappinG from a set X to a set Y such that there exists a y in Y such that there is no x in X such that x is mapped to y.
2) onto MappinG: this is MappinG from a set X to a set Y such that for every y in Y there is at least one x in X such that x is mapped to y. Such a MappinG is called a SurJection?.
3) onetoone MappinG : this is a MappinG from a set X to a set Y such that for every y in Y there is one and only one x in X such that x is mapped to y. Such a mapping is called an InJection?.
4) Further, a MappinG that is both "onto" and "onetoone," or is both a SurJection? and an InJection? is called a BiJection.
Examples:
In terms of formal SetTheory, a Mapping from X to Y is usually defined as a MathematicalRelation where each x in X is related to one, and only one, element of Y. This element is the image of x. However, there are lots of other equivalent definitions.