Difference between revisions of "Surjection"
From Encyclopedia of Mathematics
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: $ f(A)=B $, i.e., for each $ b \in B $ there is an $ a \in A $ such that $ f(a)=b $. | : $ f(A)=B $, i.e., for each $ b \in B $ there is an $ a \in A $ such that $ f(a)=b $. | ||
A function that is both surjective and [[injective]] is called [[bijective]] | A function that is both surjective and [[injective]] is called [[bijective]] | ||
| − | (or, in some contexts, a [[permutation of a set|permutation]]). | + | (or, if domain and range coincide, in some contexts, a [[permutation of a set|permutation]]). |
Revision as of 02:23, 14 February 2012
A function (or mapping) is called surjective if the image of its domain coincides with its range.
In other words, a function $ f : A \to B $ from a set $A$ to a set $B$ is
- a surjective function or a surjection or a function onto $A$
iff
- $ f(A)=B $, i.e., for each $ b \in B $ there is an $ a \in A $ such that $ f(a)=b $.
A function that is both surjective and injective is called bijective (or, if domain and range coincide, in some contexts, a permutation).
How to Cite This Entry:
Surjection. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Surjection&oldid=21022
Surjection. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Surjection&oldid=21022
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article