# Bijective

A function $f$ from set $A$ to set $B$ is called a bijection and $f$ is said to be bijective if every element in $A$ maps to a different element in $B$, and every element in $B$ is mapped onto by some element in $A$.

In symbols, if $f(x)=f(y)$, then $x=y$, and for every $y\in B$, there is some $x\in A$ with $f(x)=y$.

Therefore a bijective function is one which is both injective and surjective.

A bijection creates a correspondence between the sets $A$ and $B$: every element in $A$ corresponds to exactly one element of $B$, and vice versa.

A bijection has an inverse.