bijective

Adjective

 * 1)  Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain. (formally) Both injective and surjective.
 * 2) * 1987, James S. Royer, A Connotational Theory of Program Structure, Springer, 273, page 15,
 * Then, by a straightforward, computable, bijective numerical coding, this idealized FORTRAN determines an EN.[ ] (Note: In this FORTRAN example, we could have omitted restrictions on I/O and instead used a computable, bijective, numerical coding for inputs and outputs to get another EN determined by FORTRAN.)
 * 1) * 1993, Susan Montgomery, Hopf Algebras and Their Actions on Rings,, , Regional Conference Series in Mathematics, Number 83, page 124,
 * Recent experience indicates that for infinite-dimensional Hopf algebras, the “right” definition of Galois is to require that $$\beta$$ be bijective.
 * 1) * 2008, B. Aslan, M. T. Sakalli, E. Bulus, Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings, Joachim von zur Gathen, José Luis Imana, Çetin Kaya Koç (editors), Arithmetic of Finite Fields: 2nd International Workshop, Springer, 5130, page 131,
 * Generally, there is a parallel relation between the maximum differential value and maximum LAT value for bijective S-boxes.
 * 1) * 2012 [Introduction to Graph Theory, McGraw-Hill], Gary Chartrand, Ping Zhang, A First Course in Graph Theory, 2013, Dover, Revised and corrected republication, page 64,
 * The proof that isomorphism is an equivalence relation relies on three fundamental properties of bijective functions (functions that are one-to-one and onto): (1) every identity function is bijective, (2) the inverse of every bijective function is also bijective, (3) the composition of two bijective functions is bijective.
 * 1)  Having a component that is (specified to be) a bijective map; that specifies a bijective map.
 * 1)  Having a component that is (specified to be) a bijective map; that specifies a bijective map.

Usage notes

 * Bijective functions are invertible, and their inverses are themselves bijective functions. In particular, if a bijective map exists from one set to another, the reverse is necessarily true. Pairs of sets which admit a bijection from one to the other are said to be in bijection, in bijective correspondence, or (in the context of cardinality) equinumerous.
 * A bijective map is often called a.
 * A bijective map from a set (usually, but not exclusively, a finite set) to itself may be called a.

Translations

 * Catalan: bijectiu
 * Chinese:
 * Mandarin: 一一映射的, 双射的
 * Czech: bijektivní
 * Danish: bijektiv
 * Dutch: bijectief
 * Finnish:
 * French:
 * German: ,
 * Hungarian:, kölcsönösen egyértelmű
 * Irish: détheilgeach
 * Italian: biiettivo, bigettivo
 * Japanese: 全単射の
 * Portuguese: bijetivo
 * Romanian: bijectiv
 * Spanish: biyectivo
 * Swedish:


 * Finnish: