Every surjective function from S onto itself is one-to-one.

A surjective function can reach any element of its codomain, but not all functions do.

A surjective function is often called onto because the range fits perfectly on to the codomain.

Specifically, surjective functions are precisely the epimorphisms in the category of sets.

The proposition that every surjective function has a right inverse is equivalent to the axiom of choice.

Epimorphisms are analogues of surjective functions, but they are not exactly the same.

In a 3D video game vectors are projected onto a 2D flat screen by means of a surjective function.

Every surjective function has a right inverse.

A surjective function is a function whose image is equal to its codomain.

In whole-world presentation, the back and front hemispheres overlap, making the projection a surjective function.

Bourbaki uses epimorphism as shorthand for a surjective function.

A surjective function is a surjection.

For every , it is impossible that , because otherwise we could define a surjective function from to .

The following theorem gives equivalent formulations in terms of a bijective function or a surjective function.

Either S is empty or there exists a surjective function g : N S.

Surjective functions and families are formally equivalent, as any function f with domain I induces a family (f(i)).

Any surjective function induces a bijection defined on a quotient of its domain by collapsing all arguments mapping to a given fixed image.

This exponential map is clearly a surjective function from R to T. It is not, however, injective.

For each surjective function f : N X, its orbit under permutations of X has x!

Given finite sets A and B, how many surjective functions (onto functions) are there from A to B?

To say that the domain is finite, use the sentence that says that every surjective function from the domain to itself is injective.

In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function.

A surjective function, or surjection is a function in math which maps to every element in its codomain from its domain.

It is in general smaller than the codomain; it is the whole codomain if and only if f is a surjective function.

The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (A).