Bijection

Pronunciation

• IPA: /baɪ.dÊ’É›k.ʃən/

Origin

From French; coined by the group known as Nicolas Bourbaki in the treatise Éléments de mathématique.

Full definition of bijection

Noun

1. (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

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