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surjection
(redirected from surjections)

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surjection [sər′jek·shən]
(mathematics)
A mapping ƒ from a setAto a setBsuch that for every elementbofBthere is an elementaofAsuch that ƒ(a)=b. Also known as surjective mapping.
(mathematics)surjection - 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.

See also bijection, injection.


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