bijection
English
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bijection.svg/220px-Bijection.svg.png)
Etymology
From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.
Pronunciation
Noun
bijection (plural bijections)
- (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.
- 2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214,
Synonyms
- (function that is both a surjection and an injection): one-to-one correspondence
Translations
function that is both a surjection and an injection
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Anagrams
French
Pronunciation
Noun
bijection f (plural bijections)
- (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.
Categories:
- English terms derived from French
- English 3-syllable words
- English terms with IPA pronunciation
- English lemmas
- English nouns
- English countable nouns
- en:Set theory
- French 3-syllable words
- French terms with IPA pronunciation
- French terms with audio links
- French lemmas
- French nouns
- French countable nouns
- French feminine nouns
- fr:Set theory
- French terms with usage examples