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单词	bijection
释义	bijection /bʌɪˈdʒɛkʃ(ə)n / noun Mathematics A mapping that is both one-to-one (an injection) and onto (a surjection), i.e. a function which relates each member of a set S (the domain) to a separate and distinct member of another set T (the range), where each member in T also has a corresponding member in S.Cantor had shown that there is a bijection between the interval [0,1] and the unit square but, shortly after, Netto had proved that such a bijection cannot be continuous.... Often in combinatorics when an identity establishes the equality to two sets defined in different ways, one desires a bijection, namely, a one-to-one correspondence that converts members of one set to the other in a natural fashion. Rabh's proof defines a bijection between a disk and a triangle. Derivatives bijective adjective ... Due to the nature of the correction, the mapping is not bijective. Such a bijective proof of the Rogers-Ramanujan identities was found by Garsia and Milne by formulating an involution principle whose basic ideas can be traced to Schur's original combinatorial proof of these identities. The bijective part of the Bessel function yields the motion amplitude a.
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