injective function
We say that a function $f:A\to B$ is injective^{} or onetoone if $f(x)=f(y)$ implies $x=y$, or equivalently, whenever $x\ne y$, then $f(x)\ne f(y)$.
Properties

1.
Suppose $A,B,C$ are sets and $f:A\to B$, $g:B\to C$ are injective functions. Then the composition^{} $g\circ f$ is an injection.

2.
Suppose $f:A\to B$ is an injection, and $C\subseteq A$. Then the restriction^{} ${f}_{C}:C\to B$ is an injection.
For a list of other of injective functions, see [1].
References
 1 Wikipedia, article on http://en.wikipedia.org/wiki/Injective_functionInjective function.
Title  injective function 
Canonical name  InjectiveFunction 
Date of creation  20130322 11:51:38 
Last modified on  20130322 11:51:38 
Owner  drini (3) 
Last modified by  drini (3) 
Numerical id  16 
Author  drini (3) 
Entry type  Definition 
Classification  msc 03E20 
Classification  msc 03E99 
Synonym  onetoone 
Synonym  injection 
Synonym  embedding 
Synonym  injective 
Related topic  Bijection 
Related topic  Function 
Related topic  Surjective^{} 