bijection

plural bijections

1. mathematicsA one-to-one correspondence, a function which is both a surjection and an injection.

   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

   2 more examples

   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

   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