In combinatorics, bijective proof is a proof technique that finds a bijective function f,A ? B between two 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 more easily countable B solves the problem. 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.

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