Bijective Proof

In combinatorics, bijective proof is a proof technique that finds a bijective function f : A → B between two finite sets A and B, thus proving that they have the same number of elements, |A| = |B|. One place the technique is useful is where we wish to know the size of A, but can find no direct way of counting its elements. Then establishing a bijection from A to some B solves the problem in the case when B is more easily countable. Another useful feature of the technique is that the nature of the bijection itself often provides powerful insights into each or both of the sets.