Dictionary

bijection en · NOUN

Pronunciation

• /baɪˈd͡ʒɛk.ʃən/
• (Southern-England) audio

Etymology

PIE word *dwóh₁ From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

Meanings

1. A one-to-one correspondence, a function which is both a surjection and an injection.
   • Note in particular that a function is a bijection if and only if it's both an injection and a surjection. 2007, C. J. Date, Logic and Databases: The Roots of Relational Theory, page 167:
   • 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. 2013, William F. Basener, Topology and Its Applications, unnumbered page:
   • 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. 2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214:

Forms

Relateds

surjection · injection

Synonyms

one-to-one correspondence · bijective function

Translations (36)

ko 전단사 (function that is both a surjection and an injection) · cmn 一一映射 (function that is both a surjection and an injection) · de Bijektion (function that is both a surjection and an injection) · vi song ánh (function that is both a surjection and an injection) · nl bijectie (function that is both a surjection and an injection) · ja 全単射 (function that is both a surjection and an injection) · fi bijektio (function that is both a surjection and an injection) · ro bijecție (function that is both a surjection and an injection) · bg биекция (function that is both a surjection and an injection) · eo dissurĵeto (function that is both a surjection and an injection) · ca bijecció (function that is both a surjection and an injection) · cmn 雙射 /双射 (function that is both a surjection and an injection) · ru бие́кция (function that is both a surjection and an injection) · es biyección (function that is both a surjection and an injection) · pl funkcja wzajemnie jednoznaczna (function that is both a surjection and an injection) · de bijektive Funktion (function that is both a surjection and an injection) · sh bijekcija (function that is both a surjection and an injection) · sv bijektion (function that is both a surjection and an injection) · cs bijekce (function that is both a surjection and an injection) · pl bijekcja (function that is both a surjection and an injection) · hu kölcsönösen egyértelmű leképezés (function that is both a surjection and an injection) · sh бијекција (function that is both a surjection and an injection) · he פונקציה חד־חד־ערכית ועל (function that is both a surjection and an injection) · is gagntæk vörpun (function that is both a surjection and an injection) · et bijektsioon (function that is both a surjection and an injection) · fr bijection (function that is both a surjection and an injection) · el αμφιμονοσήμαντη αντιστοιχία (function that is both a surjection and an injection) · eo bijekcio (function that is both a surjection and an injection) · ja 双射 (function that is both a surjection and an injection) · eo inversigebla funkcio (function that is both a surjection and an injection) · io bijekto (function that is both a surjection and an injection) · ro funcție bijectivă (function that is both a surjection and an injection) · pt bijeção (function that is both a surjection and an injection) · hu bijekció (function that is both a surjection and an injection) · ca funció bijectiva (function that is both a surjection and an injection) · hi एकैकी आच्छादन (function that is both a surjection and an injection)

wikipedia: Nicolas Bourbaki · wikipedia: Éléments de mathématique