bijection

From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

• IPA^(key): /baɪˈd͡ʒɛk.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.

• bijective function
• one-to-one correspondence

• injection
• surjection

• objicient

From Latin bi- + iaciō.

• IPA^(key): /bi.ʒɛk.sjɔ̃/

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bijection f (plural bijections)

1. (set theory) bijection

   Je voudrais démontrer que cette fonction est une bijection réciproque.

   I would like to show that this function is an inverse bijection.