bijection

Etymology

PIE word *dwóh₁ From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

noun

1. (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
   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