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surjection

The Free On-line Dictionary of Computing (foldoc)

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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