Table of Contents
155 relations: Absolute space and time, Abstract rewriting system, Academic Press, Addison-Wesley, Algebra of sets, Algebraic logic, Allegory (mathematics), American Mathematical Society, Antisymmetric relation, Arithmetic, Asymmetric relation, Australia, Automata theory, Binary operation, Binary relation, Bipartite graph, Bisimulation, Block design, Block matrix, Boolean algebra (structure), C. I. Lewis, Cambridge University Press, Cartesian product, Category (mathematics), Category of relations, Category of sets, Category theory, Charles Sanders Peirce, Class (set theory), Clique (graph theory), Closure (mathematics), Complement (set theory), Complete lattice, Completeness (order theory), Composition algebra, Composition of relations, Comptes rendus de l'Académie des Sciences, Computer science, Configuration (geometry), Confluence (abstract rewriting), Congruence (geometry), Connected relation, Continent, Converse relation, Correspondence (algebraic geometry), Data mining, Database, De Gruyter, Dedekind–MacNeille completion, Dense order, ... Expand index (105 more) »
- Binary relations
Absolute space and time
Absolute space and time is a concept in physics and philosophy about the properties of the universe.
See Binary relation and Absolute space and time
Abstract rewriting system
In mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism that captures the quintessential notion and properties of rewriting systems.
See Binary relation and Abstract rewriting system
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941.
See Binary relation and Academic Press
Addison-Wesley
Addison–Wesley is an American publisher of textbooks and computer literature.
See Binary relation and Addison-Wesley
Algebra of sets
In mathematics, the algebra of sets, not to be confused with the mathematical structure of ''an'' algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion.
See Binary relation and Algebra of sets
Algebraic logic
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.
See Binary relation and Algebraic logic
Allegory (mathematics)
In the mathematical field of category theory, an allegory is a category that has some of the structure of the category Rel of sets and binary relations between them.
See Binary relation and Allegory (mathematics)
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
See Binary relation and American Mathematical Society
Antisymmetric relation
In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other.
See Binary relation and Antisymmetric relation
Arithmetic
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.
See Binary relation and Arithmetic
Asymmetric relation
In mathematics, an asymmetric relation is a binary relation R on a set X where for all a, b \in X, if a is related to b then b is not related to a.
See Binary relation and Asymmetric relation
Australia
Australia, officially the Commonwealth of Australia, is a country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands.
See Binary relation and Australia
Automata theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.
See Binary relation and Automata theory
Binary operation
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element.
See Binary relation and Binary operation
Binary relation
In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. Binary relation and binary relation are binary relations.
See Binary relation and Binary relation
Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is, every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
See Binary relation and Bipartite graph
Bisimulation
In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in that one system simulates the other and vice versa.
See Binary relation and Bisimulation
Block design
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that frequency of the elements satisfies certain conditions making the collection of blocks exhibit symmetry (balance).
See Binary relation and Block design
Block matrix
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices.
See Binary relation and Block matrix
Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.
See Binary relation and Boolean algebra (structure)
C. I. Lewis
Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher.
See Binary relation and C. I. Lewis
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
See Binary relation and Cambridge University Press
Cartesian product
In mathematics, specifically set theory, the Cartesian product of two sets and, denoted, is the set of all ordered pairs where is in and is in.
See Binary relation and Cartesian product
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows".
See Binary relation and Category (mathematics)
Category of relations
In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. Binary relation and category of relations are binary relations.
See Binary relation and Category of relations
Category of sets
In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.
See Binary relation and Category of sets
Category theory
Category theory is a general theory of mathematical structures and their relations.
See Binary relation and Category theory
Charles Sanders Peirce
Charles Sanders Peirce (September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism".
See Binary relation and Charles Sanders Peirce
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
See Binary relation and Class (set theory)
Clique (graph theory)
In the mathematical area of graph theory, a clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent.
See Binary relation and Clique (graph theory)
Closure (mathematics)
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset.
See Binary relation and Closure (mathematics)
Complement (set theory)
In set theory, the complement of a set, often denoted by A^\complement, is the set of elements not in.
See Binary relation and Complement (set theory)
Complete lattice
In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).
See Binary relation and Complete lattice
Completeness (order theory)
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).
See Binary relation and Completeness (order theory)
Composition algebra
In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies for all and in.
See Binary relation and Composition algebra
Composition of relations
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, and its result is called a relative product.
See Binary relation and Composition of relations
Comptes rendus de l'Académie des Sciences
(English: Proceedings of the Academy of Sciences), or simply Comptes rendus, is a French scientific journal published since 1835.
See Binary relation and Comptes rendus de l'Académie des Sciences
Computer science
Computer science is the study of computation, information, and automation.
See Binary relation and Computer science
Configuration (geometry)
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.
See Binary relation and Configuration (geometry)
Confluence (abstract rewriting)
In computer science and mathematics, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result.
See Binary relation and Confluence (abstract rewriting)
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
See Binary relation and Congruence (geometry)
Connected relation
In mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all pairs of elements of the set in one direction or the other while it is called strongly connected if it relates pairs of elements.
See Binary relation and Connected relation
Continent
A continent is any of several large geographical regions.
See Binary relation and Continent
Converse relation
In mathematics, the converse of a binary relation is the relation that occurs when the order of the elements is switched in the relation. Binary relation and converse relation are binary relations.
See Binary relation and Converse relation
Correspondence (algebraic geometry)
In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V×W, that is closed in the Zariski topology.
See Binary relation and Correspondence (algebraic geometry)
Data mining
Data mining is the process of extracting and discovering patterns in large data sets involving methods at the intersection of machine learning, statistics, and database systems.
See Binary relation and Data mining
Database
In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data.
See Binary relation and Database
De Gruyter
Walter de Gruyter GmbH, known as De Gruyter, is a German scholarly publishing house specializing in academic literature.
See Binary relation and De Gruyter
Dedekind–MacNeille completion
In mathematics, specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it.
See Binary relation and Dedekind–MacNeille completion
Dense order
In mathematics, a partial order or total order X is said to be dense if, for all x and y in X for which x, there is a z in X such that x. That is, for any two elements, one less than the other, there is another element between them.
See Binary relation and Dense order
Directed graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs.
See Binary relation and Directed graph
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.
See Binary relation and Divisor
Element (mathematics)
In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set.
See Binary relation and Element (mathematics)
Empty set
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
See Binary relation and Empty set
Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. Binary relation and equality (mathematics) are binary relations.
See Binary relation and Equality (mathematics)
Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
See Binary relation and Equivalence relation
Ernst Schröder (mathematician)
Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Grand Duchy of Baden – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic.
See Binary relation and Ernst Schröder (mathematician)
Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.
See Binary relation and Euclidean plane
Europe
Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere.
See Binary relation and Europe
Finitary relation
In mathematics, a finitary relation over a sequence of sets is a subset of the Cartesian product; that is, it is a set of n-tuples, each being a sequence of elements xi in the corresponding Xi.
See Binary relation and Finitary relation
Formal concept analysis
In information science, formal concept analysis (FCA) is a principled way of deriving a concept hierarchy or formal ontology from a collection of objects and their properties.
See Binary relation and Formal concept analysis
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of.
See Binary relation and Function (mathematics)
Function composition
In mathematics, function composition is an operation that takes two functions and, and produces a function such that.
See Binary relation and Function composition
Functional relation
Functional relation may refer to.
See Binary relation and Functional relation
Fundamenta Informaticae
Fundamenta Informaticae is a peer-reviewed scientific journal covering computer science.
See Binary relation and Fundamenta Informaticae
Garrett Birkhoff
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician.
See Binary relation and Garrett Birkhoff
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
See Binary relation and Geometry
Georg Aumann
Georg Aumann (11 November 1906 in Munich, Germany – 4 August 1980), was a German mathematician.
See Binary relation and Georg Aumann
Graph (discrete mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".
See Binary relation and Graph (discrete mathematics)
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
See Binary relation and Graph theory
Gunther Schmidt
Gunther Schmidt (born 1939, Rüdersdorf) is a German mathematician who works also in informatics.
See Binary relation and Gunther Schmidt
Hadamard product (matrices)
In mathematics, the Hadamard product (also known as the element-wise product, entrywise product or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
See Binary relation and Hadamard product (matrices)
Hasse diagram
In order theory, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction.
See Binary relation and Hasse diagram
Hermann Minkowski
Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, or Lithuanian-German, or Russian.
See Binary relation and Hermann Minkowski
Homogeneous relation
In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product.
See Binary relation and Homogeneous relation
Hyperbolic orthogonality
In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events.
See Binary relation and Hyperbolic orthogonality
Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices.
See Binary relation and Hypergraph
Hyperplane
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension.
See Binary relation and Hyperplane
Identity matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere.
See Binary relation and Identity matrix
If and only if
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements.
See Binary relation and If and only if
Image (mathematics)
In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f".
See Binary relation and Image (mathematics)
Incidence matrix
In mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation.
See Binary relation and Incidence matrix
Incidence structure
In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects.
See Binary relation and Incidence structure
Indicator (statistics)
In statistics and research design, an indicator is an observed value of a variable, or in other words "a sign of a presence or absence of the concept being studied".
See Binary relation and Indicator (statistics)
Infimum and supremum
In mathematics, the infimum (abbreviated inf;: infima) of a subset S of a partially ordered set P is the greatest element in P that is less than or equal to each element of S, if such an element exists.
See Binary relation and Infimum and supremum
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
See Binary relation and Integer
Integer partition
In number theory and combinatorics, a partition of a non-negative integer, also called an integer partition, is a way of writing as a sum of positive integers.
See Binary relation and Integer partition
Internet Archive
The Internet Archive is an American nonprofit digital library founded in 1996 by Brewster Kahle.
See Binary relation and Internet Archive
Intersection (set theory)
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A.
See Binary relation and Intersection (set theory)
Involution (mathematics)
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, for all in the domain of.
See Binary relation and Involution (mathematics)
Jacques Riguet
Jacques Riguet (1921 to October 20, 2013) was a French mathematician known for his contributions to algebraic logic and category theory.
See Binary relation and Jacques Riguet
Jakob Steiner
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry.
See Binary relation and Jakob Steiner
Ki-Hang Kim
Ki-Hang Kim (5 August 1936 – 15 January 2009), also known as Kim Ki-Hang Butler, Hang Kim, Keyhany Keem, or Kim Ki-Hang was a Korean-American Mathematician and Alabama State University professor known for his contributions in semigroups, Boolean matrices, and Social Sciences.
See Binary relation and Ki-Hang Kim
Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
See Binary relation and Lattice (order)
Law of trichotomy
In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero.
See Binary relation and Law of trichotomy
Lecture Notes in Computer Science
Lecture Notes in Computer Science is a series of computer science books published by Springer Science+Business Media since 1973.
See Binary relation and Lecture Notes in Computer Science
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.
See Binary relation and Linear algebra
Logical matrix
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets.
See Binary relation and Logical matrix
Marcel Dekker
Marcel Dekker was a journal and encyclopedia publishing company with editorial boards found in New York City.
See Binary relation and Marcel Dekker
Mary P. Dolciani
Mary P. Dolciani (1923–1985) was an American mathematician, known for her work with secondary-school mathematics teachers.
See Binary relation and Mary P. Dolciani
Matematicheskii Sbornik
Matematicheskii Sbornik (Математический сборник, abbreviated Mat. Sb.) is a peer reviewed Russian mathematical journal founded by the Moscow Mathematical Society in 1866.
See Binary relation and Matematicheskii Sbornik
Mathematical Reviews
Mathematical Reviews is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science.
See Binary relation and Mathematical Reviews
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Binary relation and Mathematics
Matrix addition
In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together.
See Binary relation and Matrix addition
Matrix multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices.
See Binary relation and Matrix multiplication
Matrix of ones
In mathematics, a matrix of ones or all-ones matrix has every entry equal to one.
See Binary relation and Matrix of ones
Matrix ring
In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication.
See Binary relation and Matrix ring
Module homomorphism
In algebra, a module homomorphism is a function between modules that preserves the module structures.
See Binary relation and Module homomorphism
Morphism
In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures, functions from a set to another set, and continuous functions between topological spaces.
See Binary relation and Morphism
Morse–Kelley set theory
In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG).
See Binary relation and Morse–Kelley set theory
Multivalued function
In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least one point in its domain.
See Binary relation and Multivalued function
Naive set theory
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics.
See Binary relation and Naive set theory
Natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.
See Binary relation and Natural number
Ocean
The ocean is the body of salt water that covers approx.
Order theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations.
See Binary relation and Order theory
Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
See Binary relation and Ordered pair
Ordinal number
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets.
See Binary relation and Ordinal number
Orthogonality
In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.
See Binary relation and Orthogonality
Outer product
In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector.
See Binary relation and Outer product
Partial equivalence relation
In mathematics, a partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is symmetric and transitive.
See Binary relation and Partial equivalence relation
Partial function
In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to.
See Binary relation and Partial function
Partially ordered set
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. Binary relation and Partially ordered set are binary relations.
See Binary relation and Partially ordered set
Polish notation
Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow their operands.
See Binary relation and Polish notation
Power set
In mathematics, the power set (or powerset) of a set is the set of all subsets of, including the empty set and itself.
See Binary relation and Power set
Preorder
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.
See Binary relation and Preorder
Primary key
In the relational model of databases, a primary key is a specific choice of a minimal set of attributes (columns) that uniquely specify a tuple (row) in a relation (table).
See Binary relation and Primary key
Prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.
See Binary relation and Prime number
Rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
See Binary relation and Rational number
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
See Binary relation and Real number
Reflexive closure
In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive relation on X that contains R. A relation is called if it relates every element of X to itself. Binary relation and reflexive closure are binary relations.
See Binary relation and Reflexive closure
Reflexive relation
In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.
See Binary relation and Reflexive relation
Relation (mathematics)
In mathematics, a relation on a set may, or may not, hold between two given members of the set.
See Binary relation and Relation (mathematics)
Rudolf Berghammer
Rudolf Berghammer (born 1952 in Oberndorf, Germany) is a German mathematician who works in computer science.
See Binary relation and Rudolf Berghammer
Russell's paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901.
See Binary relation and Russell's paradox
Semigroup with involution
In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group.
See Binary relation and Semigroup with involution
Semiring
In abstract algebra, a semiring is an algebraic structure.
See Binary relation and Semiring
Serial relation
In set theory a serial relation is a homogeneous relation expressing the connection of an element of a sequence to the following element.
See Binary relation and Serial relation
Set (mathematics)
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
See Binary relation and Set (mathematics)
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.
See Binary relation and Set theory
Split-complex number
In algebra, a split complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit satisfying j^2.
See Binary relation and Split-complex number
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
See Binary relation and Springer Science+Business Media
Steiner system
The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ.
See Binary relation and Steiner system
Subset
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).
See Binary relation and Subset
Symmetric relation
A symmetric relation is a type of binary relation.
See Binary relation and Symmetric relation
Ternary operation
In mathematics, a ternary operation is an n-ary operation with n.
See Binary relation and Ternary operation
Total order
In mathematics, a total order or linear order is a partial order in which any two elements are comparable.
See Binary relation and Total order
Total relation
In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain.
See Binary relation and Total relation
Transitive closure
In mathematics, the transitive closure of a homogeneous binary relation on a set is the smallest relation on that contains and is transitive. Binary relation and transitive closure are binary relations.
See Binary relation and Transitive closure
Transitive relation
In mathematics, a binary relation on a set is transitive if, for all elements,, in, whenever relates to and to, then also relates to.
See Binary relation and Transitive relation
Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
See Binary relation and Union (set theory)
Upper and lower bounds
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of.
See Binary relation and Upper and lower bounds
Viktor Wagner
Viktor Vladimirovich Wagner, also Vagner (Виктор Владимирович Вагнер) (4 November 1908 – 15 August 1981) was a Russian mathematician, best known for his work in differential geometry and on semigroups.
See Binary relation and Viktor Wagner
Von Neumann–Bernays–Gödel set theory
In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC).
See Binary relation and Von Neumann–Bernays–Gödel set theory
Weak ordering
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other.
See Binary relation and Weak ordering
Zero matrix
In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero.
See Binary relation and Zero matrix
See also
Binary relations
- Accessibility relation
- Ancestral relation
- Apartness relation
- BIT predicate
- Binary operations
- Binary relation
- Category of relations
- Comparability
- Congruence relation
- Converse relation
- Countable Borel relation
- Covering relation
- Dependence relation
- Directed set
- Equality (mathematics)
- Equipollence (geometry)
- Equivalence class
- FNP (complexity)
- Inequalities
- Join and meet
- Partially ordered set
- Quotient by an equivalence relation
- Rational consequence relation
- Reflexive closure
- Separoid
- Symmetric closure
- TFNP
- Transitive closure
References
Also known as Afterset, Asymmetrical relationship, Binary predicate, Binary relation on a set, Binary relation over a set, Binary relations, Contact relation, Difunctional, Difunctional relation, Domain of a relation, Dyadic relation, Field of a relation, Foreset, Fringe of a relation, Heterogeneous relation, Heterorelativ, Injective relation, Left-unique relation, Many-to-many relation, Many-to-one relation, Mathematical Relationships, Mathematical relation, Mathematical relationship, MathematicalRelation, One-to-many relation, One-to-one relation, Onto relation, Operations on binary relations, Range of a relation, Rectangular relation, Relation on a set, Relational mathematics, Restriction relation, Right total, Right total relation, Right-definite relation, Right-total, Right-total relation, Right-unique, Right-unique relation, Set-like relation, Surjective relation, Two-place relation, Univalent relation.