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A bijection.


From French; coined by the group known as Nicolas Bourbaki in the treatise Éléments de mathématique.


  • IPA(key): /baɪ.dʒɛk.ʃən/


bijection (plural bijections)

  1. (set theory) A one-to-one correspondence, a function which is both a surjection and an injection.
    • 2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214,
      The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.
    • 2007, C. J. Date, Logic and Databases: The Roots of Relational Theory, page 167,
      Note in particular that a function is a bijection if and only if it's both an injection and a surjection.
    • 2013, William F. Basener, Topology and Its Applications, unnumbered page,
      The basic idea is that two sets A and B have the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.





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bijection f (plural bijections)

  1. (set theory) bijection
    Je voudrais démontrer que cette fonction est une bijection réciproque.
    (please add an English translation of this usage example)