Definition:Surjection

A mapping $$f$$ is described as onto, or a surjection, or surjective, if:

$$\forall y \in \mathrm{Rng} \left({f}\right): \exists x \in \mathrm{Dom} \left({f}\right): f \left({x}\right) = y$$

That is, every element in the range of $$f$$ is mapped to by at least one element in the domain.

If $$f$$ is not a surjection, then $$f$$ is described as into.