Injective function

From Citizendium, the Citizens' Compendium

Jump to: navigation, search


This article is a stub and thus not approved.
Main Article
Talk
Related Articles  [?]
Bibliography  [?]
External Links  [?]
 
http://en.citizendium.org/wiki?title=Injective_function&printable=yes
This is a draft article, under development and not meant to be cited but you can help to improve it. These unapproved articles are subject to a disclaimer.

In mathematics, an injective function or one-to-one function or injection is a function which has different output values on different input values: f is injective if x_1 \neq x_2 implies that f(x_1) \neq f(x_2).

An injective function f has a well-defined partial inverse f − 1. If y is an element of the image set of f, then there is at least one input x such that f(x) = y. If f is injective then this x is unique and we can define f − 1(y) to be this unique value. We have f − 1(f(x)) = x for all x in the domain.

A strictly monotonic function is injective, since in this case x1 < x2 implies that f(x1) < f(x2).

See also

Retrieved from "http://en.citizendium.org/wiki/Injective_function"
Views
Personal tools