surjection
onto
surjective
<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)