Bijection

"Bijective function" redirects here. For other uses, see Bijective function (disambiguation).

A bijection (or bijective function) is a function that is both injective and surjective. A bijection is sometimes called a one-to-one mapping, or a one-to-one correspondence.

This is the same as saying: a function $f$ with domain $A$ and codomain $B$ is bijective if and only if $f(x)$ and $f(y)$ are different whenever $x$ and $y$ are different, and every element $z$ of $B$ has an element $x$ of $A$ where $f(x)=z$.

If $f$ is a bijection from $A$ to $B$ then its inverse, $f^{-1}$, is a bijection from $B$ to $A$.