onto

Etymology

From on + to, after into. Compare Saterland Frisian antou (“up to”).

prep

1. Arriving upon or on top of (speaking of a physical or metaphorical movement).
   My cat just jumped onto the keyboard.
   Private-equity nabobs bristle at being dubbed mere financiers. Piling debt onto companies’ balance-sheets is only a small part of what leveraged buy-outs are about, they insist. Improving the workings of the businesses they take over is just as core to their calling, if not more so. Much of their pleading is public-relations bluster. 2013-06-22, “Engineers of a different kind”, in The Economist, volume 407, number 8841, page 70
2. (informal) Aware of.
   The thought-police were onto my plans of world domination.
3. (mathematics) Being an onto function with a codomain of (see below).
   The exponential function maps the set of real numbers onto the set of positive real numbers.

adj

1. (mathematics, of a function) Assuming each of the values in its codomain; having its range equal to its codomain.
   Considered as a function on the real numbers, the exponential function is not onto.