bijection

A bijection, or a bijective function, is a function $f:A\to B$ that is both injective and surjective, i.e., each element $b\in B$ is the value of $f(a)$ for exactly one $a\in A$. By definition, if a bijection exists between $A$ and $B$, $|A|=|B|$.

Since bijections are injective, they also have inverse (function) functions. Inverse of bijections are also bijections.