From The Collaborative International Dictionary of English v.0.48 :
Onto \On"to\, prep. [On + to. Cf. Into.]
On the top of; upon; on. See On to, under On, prep.
[1913 Webster] Ontogenesis
From The Free On-line Dictionary of Computing (30 December 2018) :
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)