bijection
English edit
Etymology edit
PIE word |
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*dwóh₁ |
From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.
Pronunciation edit
Noun edit
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.
Synonyms edit
Related terms edit
Translations edit
function that is both a surjection and an injection
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Anagrams edit
French edit
Etymology edit
Pronunciation edit
Noun edit
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.