Bijective
English
Pronunciation
Adjective
- Template:Lb 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; Template:Lb both injective and surjective.
- 1987, James S. Royer, A Connotational Theory of Program Structure, Springer, Template:W 273, page 15,
- Then, by a straightforward, computable, bijective numerical coding, this idealized FORTRAN determines an EN.[Template:W] (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, Template:W, Template:W, 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 be bijective.
- 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, Template:W 5130, page 131,
- Generally, there is a parallel relation between the maximum differential value and maximum LAT value for bijective S-boxes.
- Template:Quote-book
- 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.
- 1987, James S. Royer, A Connotational Theory of Program Structure, Springer, Template:W 273, page 15,
- Template:Lb 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 Template:M.
- A bijective map from a set (usually, but not exclusively, a finite set) to itself may be called a Template:M.
Derived terms
Related terms
Translations
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