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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'', 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. 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.
==Basic examples==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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