Mathematics-Online course: Preparatory Course Mathematics-Basics-Mappings-Properties of Mappings

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	Mathematics-Online course: Preparatory Course Mathematics - Basics - Mappings
	Properties of Mappings

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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)

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automatically generated 1/9/2017