injective function

We say that a function f:AB is injectivePlanetmathPlanetmath or one-to-one if f(x)=f(y) implies x=y, or equivalently, whenever xy, then f(x)f(y).


  1. 1.

    Suppose A,B,C are sets and f:AB, g:BC are injective functions. Then the compositionMathworldPlanetmath gf is an injection.

  2. 2.

    Suppose f:AB is an injection, and CA. Then the restrictionPlanetmathPlanetmathPlanetmath f|C:CB is an injection.

For a list of other of injective functions, see [1].


  • 1 Wikipedia, article on 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 SurjectivePlanetmathPlanetmath