I. |ȯntə, |än-, -n.tu̇, -n.(ˌ)tü, +V often -ntəw preposition
Etymology: on (II) + to
1.
a. : to a position or point on or upon
slipped away from the chair onto the floor — C.D.Lewis
water splashed down from the roof onto my hat — Joseph Wechsberg
jumped off the boat and onto the dock
climbed out onto the roof
b. chiefly dialect : in position on
the coat has big buttons onto it — Delia H. Pugh
2. : in or into a state of awareness or knowledgeability about
he's a shrewd bird and he's onto me — Mark Schorer
was onto something that should have been pursued further — Bosley Crowther
— compare on II 8
II. preposition
— used as a function word which precedes a word or phrase denoting a set each element of which is the image of at least one element of another set
a function mapping the set S onto the set T
III. ˈȯn(ˌ)tü, ˈän- adjective
Etymology: onto , preposition (herein)
: mapping elements in such a way that every element in one set is the image of at least one element in another set
a function that is one-to-one and onto
— see surjection herein