injective function

We say that a function $f\colon A\to B$ is injective or one-to-one if $f(x)=f(y)$ implies $x=y$ , or equivalently, whenever $x\neq y$ , then $f(x)\neq f(y)$ .

Properties

1.

Suppose $A, B, C$ are sets and $f\colon A\to B$ , $g\colon B\to C$ are injective functions. Then the composition $g\circ f$ is an injection.
2.

Suppose $f\colon A\to B$ is an injection, and $C\subseteq A$ . Then the restriction $f|_{C}\colon C\to B$ 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	2013-03-22 11:51:38
Last modified on	2013-03-22 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	one-to-one
Synonym	injection
Synonym	embedding
Synonym	injective
Related topic	Bijection
Related topic	Function
Related topic	Surjective