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In combinatorics, bijective proof is a proof technique that finds a bijective function (that is, a one-to-one and onto function) f : A → B between two finite sets A and B, or a size-preserving bijective function between two combinatorial classes, 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. By establishing a bijection from A to some B solves the problem if 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.

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• Bijective proof
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• In combinatorics, bijective proof is a proof technique that finds a bijective function (that is, a one-to-one and onto function) f : A → B between two finite sets A and B, or a size-preserving bijective function between two combinatorial classes, 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. By establishing a bijection from A to some B solves the problem if 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.
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• In combinatorics, bijective proof is a proof technique that finds a bijective function (that is, a one-to-one and onto function) f : A → B between two finite sets A and B, or a size-preserving bijective function between two combinatorial classes, 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. By establishing a bijection from A to some B solves the problem if 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.
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