# Empty Mapping to Empty Set is Bijective

## Theorem

Let $\nu: \O \to \O$ be an empty mapping.

Then $\nu$ is a bijection.

## Proof

From Empty Mapping is Injective, $\nu$ is injective.

As the codomain of $\nu$ is empty, $\nu$ is vacuously surjective.

$\blacksquare$