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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
surjection
onto
surjective
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)