Surjection



noun, Mathematics.
1.
onto function.
noun
1.
a mathematical function or mapping for which every element of the image space is a value for some members of the domain See also injection (sense 5), bijection
surjection
(sər-jěk’shən)
A function such that each member of its range is mapped onto by a member of the domain. Compare bijection, injection.

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.
See also bijection, injection.
(1995-05-27)

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