bijective
EnglishEdit
PronunciationEdit
 Rhymes: ɛktɪv
AdjectiveEdit
bijective (not comparable)
 (mathematics, of a map) Both injective and surjective.
 1987, James S. Royer, A Connotational Theory of Program Structure, Springer, LNCS 273, page 15,
 Then, by a straightforward, computable, bijective numerical coding, this idealized FORTRAN determines an EN.^{[effective numbering]} (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.)
 1993, Susan Montgomery, Hopf Algebras and Their Actions on Rings, American Mathematical Society, CBMS, Regional Conference Series in Mathematics, Number 83, page 124,
 Recent experience indicates that for infinitedimensional Hopf algebras, the “right” definition of Galois is to require that be bijective.
 2008, B. Aslan, M. T. Sakalli, E. Bulus, Classifying 8Bit to 8Bit SBoxes Based on Power Mappings, Joachim von zur Gathen, José Luis Imana, Çetin Kaya Koç (editors), Arithmetic of Finite Fields: 2nd International Workshop, Springer, LNCS 5130, page 131,
 Generally, there is a parallel relation between the maximum differential value and maximum LAT value for bijective Sboxes.
 2010, Kang Feng, Mengzhao Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Springer, page 39,
 An isomorphism is a bijective homomorphism.
 2012 [Introduction to Graph Theory, McGrawHill], 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 onetoone 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.
 1987, James S. Royer, A Connotational Theory of Program Structure, Springer, LNCS 273, page 15,
 (mathematics) Having a component that is (specified to be) a bijective map; that specifies a bijective map.
Usage notesEdit
 If a bijective map exists from one set to another, the reverse is necessarily true, and the sets are said to be in bijective (also onetoone) correspondence.
 A bijective map is often called a bijection.
 A bijective map from a set (usually, but not exclusively, a finite set) to itself may be called a permutation.
Derived termsEdit
Related termsEdit
TranslationsEdit
both injective and surjective

having a bijective map

Further readingEdit
 Bijection, injection and surjection on Wikipedia.Wikipedia
 Bijective numeration on Wikipedia.Wikipedia
 Bijective proof on Wikipedia.Wikipedia
 Homomorphism#Isomorphism on Wikipedia.Wikipedia
See alsoEdit
FrenchEdit
PronunciationEdit
 IPA^{(key)}: /bi.ʒɛk.tiv/
 Homophone: bijectives
AdjectiveEdit
bijective