surjection

surjection

[ser-jek-shuhn]
noun Mathematics.

Origin:
1960–65; sur-1 + -jection, as in injection, projection, etc.

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World English Dictionary
 surjection (sɜːˈdʒɛkʃən) —n injection See also bijection a mathematical function or mapping for which every element of the image space is a value for some members of the domain [C20: from sur-1 + -jection, on the model of projection] sur'jective —adj

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Science Dictionary
 surjection  [%PREMIUM_LINK%]     (sər-jěk'shən)  Pronunciation Key  A function such that each member of its range is mapped onto by a member of the domain. Compare bijection, injection.
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surjection definition

mathematics
A function f : A -> B is surjective or onto or a surjection if f A = B. I.e. f can return any value in B. This means that its image is its codomain.
Only surjections have right inverses, f' : B -> A where f (f' x) = x since if f were not a surjection there would be elements of B for which f' was not defined.