bijection

Pronunciation

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Pronunciation

- IPA: /baɪ.dʒɛk.ʃən/

**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**.

- The present text has defined a set to be finite if and only if there exists a
**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.

- Note in particular that a function is a
**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.

- The basic idea is that two sets A and B have

- (
*function that is both a surjection and an injection*) one-to-one correspondence

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004