Mathematics-Online lexicon: Properties of Mappings

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Properties of Mappings

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

overview

A map

$\displaystyle f: A \longrightarrow B$

between two sets

and

is called

injective, if $f(a) \neq f(a')$ for all $a,a' \in A$ , $a \neq a'$
surjective, if for all $b \in B$ there is an $a \in A$ such that
bijective, if is both injective and surjective.

These notions can be illustrated by the following diagrams:

$\includegraphics[clip,width=.3\linewidth]{injektiv_Bild}$
$\includegraphics[clip,width=.3\linewidth]{surjektiv_Bild}$

$\includegraphics[clip,width=.3\linewidth]{bijektiv_Bild}$

injective surjective bijective

(Authors: Kimmerle/Abele)

[Examples] [Links]

automatically generated 6/11/2007