# 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. 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. 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