Assuming each of the values in its codomain; having its range equal to its codomain.
"The function is onto because every element in the codomain has a corresponding value from the domain."
In plain English: Onto describes something that is on top of another surface and usually stays there securely.
"He jumped onto the moving train before the doors closed."
Usage: This term is strictly mathematical and does not have an everyday meaning as an adjective, so it should only be used when discussing functions where every element in the target set has a corresponding input. Do not use "onto" for general descriptions of movement or location; instead, rely on the preposition form to indicate direction toward a surface.
Upon; on top of.
"She climbed onto the roof to fix the leaky chimney."
The word onto is formed by combining the prepositions on and to, appearing later than its synonym into. It functions as a single unit indicating movement or direction toward a surface or position above something else.