Bijective Function

Definition

A function \(f : X \to Y\) is said to be bijective or is called a bijection if it is both surjective and injective


This is equivalent to the fact that for every \(y \in Y\), there exists a unique \(x \in X\) such that \(f(x) = y\).

Bijective functions give a one to one correspondence between every element in \(X\) and \(Y\), and hence bijectivity is both a sufficient and necessary condition for the function to be invertible.