bijection
noun/baɪˈd͡ʒɛk.ʃən/
Etymology PIE word *dwóh₁ From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.
1
Mathematics, Sciences, Set theory A one-to-one correspondence, a function which is both a surjection and an injection.
- 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:
- 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:
1 more example
- 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:
- Synonyms
- bijective function, one-to-one correspondence
- Related terms
- injection, surjection