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单词 bijection
释义

Definition of bijection in English:

bijection

noun bʌɪˈdʒɛkʃ(ə)n
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.

    Example sentencesExamples
    • 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.
    • In fact, it is easy to see that this bijection provides a conjugacy.
    • Rabh's proof defines a bijection between a disk and a triangle.

Derivatives

  • bijective

  • adjective
    Mathematics
    • The bijective part of the Bessel function yields the motion amplitude a.
      Example sentencesExamples
      • 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.
      • Due to the nature of the correction, the mapping is not bijective.
 
 
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更新时间:2024/12/23 20:28:28