onto

Meanings

1. 1
   prep

   Arriving upon or on top of (speaking of a physical or metaphorical movement).

   My cat just jumped onto the keyboard.

2. 2
   prep

   Aware of.

   The thought-police were onto my plans of world domination.

3. 3
   prep

   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.

4. 4
   adj

   Attaining each of the values in its codomain; having its image equal to its codomain.

   Considered as a function on the real numbers, the exponential function is not onto, as it never takes on values less than or equal to zero.

Etymology

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