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Difference between revisions of "Surjection"

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''surjective mapping, from a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914201.png" /> onto a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914202.png" />''
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''surjective mapping, from a set $A$ onto a set $B$''
  
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A mapping <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914203.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914204.png" />, i.e. such that for each <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914205.png" /> there is an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914206.png" /> with <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091420/s0914207.png" />. As well as saying  "f is surjective" , one can also say  "f is a mapping from A onto B" .
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A mapping $f$ such that $f(A)=B$, i.e. such that for each $b\in B$ there is an $a\in A$ with $f(a)=b$. As well as saying  "$f$ is surjective" , one can also say  "$f$ is a mapping from $A$ onto $B$" .
  
  

Revision as of 22:26, 13 February 2012

surjective mapping, from a set $A$ onto a set $B$

A mapping $f$ such that $f(A)=B$, i.e. such that for each $b\in B$ there is an $a\in A$ with $f(a)=b$. As well as saying "$f$ is surjective" , one can also say "$f$ is a mapping from $A$ onto $B$" .


Comments

See also Injection; Bijection; Permutation of a set.

How to Cite This Entry:
Surjection. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Surjection&oldid=21018
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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