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.
