bijection

English

A bijection.

Etymology

PIE word
*dwóh₁

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

Pronunciation

• IPA^(key): /baɪˈd͡ʒɛk.ʃən/

Noun

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.

Synonyms

• bijective function
• one-to-one correspondence

Related terms

• injection
• surjection

Translations

function that is both a surjection and an injection

• Catalan: funció bijectiva f, bijecció f
• Chinese:

  Mandarin: 一一映射 (yīyīyìngshè), 雙射／双射 (zh) (shuāngshè)

• Czech: bijekce f
• Dutch: bijectie (nl) f
• Esperanto: dissurĵeto, inversigebla funkcio, bijekcio
• Estonian: bijektsioon
• Finnish: bijektio (fi)
• French: bijection (fr) f
• German: Bijektion f, bijektive Funktion f
• Greek: αμφιμονοσήμαντη αντιστοιχία f (amfimonosímanti antistoichía)
• Hebrew: פונקציה חד-חד-ערכית ועל f
• Hindi: एकैकी आच्छादन (ekaikī ācchādan)
• Hungarian: bijekció (hu), kölcsönösen egyértelmű leképezés (hu)
• Icelandic: gagntæk vörpun f
• Ido: bijekto
• Japanese: 全単射 (ja) (ぜんたんしゃ, zentansha), 双射 (ja) (そうしゃ, sōsha)
• Korean: 전단사 (jeondansa)
• Polish: bijekcja (pl) f, funkcja wzajemnie jednoznaczna (pl) f
• Portuguese: bijeção (pt) f
• Romanian: bijecție f, funcție bijectivă f
• Russian: бие́кция (ru) f (bijékcija)
• Serbo-Croatian: bijekcija (sh) f, бијекција f
• Spanish: biyección (es) f
• Swedish: bijektion (sv) c

Anagrams

• objicient

French

Etymology

From Latin bi- + iaciō.

Pronunciation

• IPA^(key): /bi.ʒɛk.sjɔ̃/

• Audio (Paris)

  (file)

• Audio

  (file)

Noun

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.