# bijection

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## English

English Wikipedia has an article on:
Wikipedia

### 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. 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.

## French

### Etymology

From Latin bi- + iaciō.

### Pronunciation

• IPA(key): /bi.ʒɛk.sjɔ̃/
•  Audio (Paris) (file)
•  Audio (file)

### Noun

bijection f (plural bijections)

1. bijection
Je voudrais démontrer que cette fonction est une bijection réciproque.
I would like to show that this function is an inverse bijection.