Onto vs. Surjective

Onto vs. Surjective — Is There a Difference?

Difference Between Onto and Surjective

Ontopreposition

On top of; to a position on; upon

The dog jumped onto the chair.

Surjectiveadjective

(mathematics) of, relating to, or being a surjection

Ontopreposition

(Informal) Fully aware of; informed about

The police are onto the robbers' plans.

Ontoadjective

Of, relating to, or being a function such that every element of the codomain is the value that corresponds to an element in the domain.

Ontopreposition

Upon; on top of.

My cat just jumped onto the keyboard.

Ontopreposition

(informal) Aware of.

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

Ontopreposition

(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.

Ontoadjective

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.