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Relationship between elements of two sets
In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set (possibly the same) called the
Binary_relation
Binary relation over a set and itself
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
Homogeneous_relation
Mathematical concept for comparing objects
mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in
Equivalence_relation
Operation on the subsets of a set
single element under ideal operations is called a principal ideal. A binary relation R {\displaystyle R} on a set A {\displaystyle A} is a subset of A ×
Closure_(mathematics)
Type of binary relation
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates
Transitive_relation
Type of binary relation
A symmetric relation is a type of binary relation. A homogeneous relation R {\displaystyle R} on a set X {\displaystyle X} is symmetric if: for all a
Symmetric_relation
Property that assigns truth values to k-tuples of individuals
Rx1⋯xn and using postfix notation by x1⋯xnR. In the case where R is a binary relation, those statements are also denoted using infix notation by x1Rx2. The
Finitary_relation
Type of binary relation
In mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a set or, more generally, a class X if every non-empty
Well-founded_relation
Topics referred to by the same term
Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial
Relation
Relation of degree three
a binary relation is formally defined as a set of pairs, i.e. a subset of the Cartesian product A × B of some sets A and B, so a ternary relation is
Ternary_relation
Mathematical function with no sudden changes
canonically identified with the quotient topology under the equivalence relation defined by f {\displaystyle f} . Dually, for a function f {\displaystyle
Continuous_function
Relationship between two sets, defined by a set of ordered pairs
(finitary relation, like "person x lives in town y at time z"), and relations between classes (like "is an element of" on the class of all sets, see Binary relation
Relation_(mathematics)
Type of binary relation
In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle
Antisymmetric_relation
Reversal of the order of elements of a binary relation
a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of'
Converse_relation
Binary relation that relates every element to itself
In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is reflexive if it relates every element of X {\displaystyle X} to
Reflexive_relation
Matrix of binary truth values
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a
Logical_matrix
Association of one output to each input
establishes a relation between the elements of the domain and some (possibly all) elements of the codomain. Mathematically, a binary relation between two
Function_(mathematics)
Number of arguments required by a function
arguments. Mathematics portal Philosophy portal Logic of relatives Binary relation Ternary relation Theory of relations Signature (logic) Parameter p-adic number
Arity
Type of logical 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 {x : there is a y with
Total_relation
Function with a smaller domain
A\triangleleft R} of a binary relation R {\displaystyle R} between E {\displaystyle E} and F {\displaystyle F} may be defined as a relation having domain A
Restriction_(mathematics)
Binary relation in computer science
dependency relation is a symmetric and reflexive binary relation on a finite domain Σ {\displaystyle \Sigma } ; i.e. a finite tolerance relation. That is
Dependency_relation
Reflexive and transitive binary relation
mathematics, in particular in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest
Preorder
Binary relation which never occurs in both directions
In mathematics, an asymmetric relation is a binary relation R {\displaystyle R} on a set X {\displaystyle X} where for all a , b ∈ X , {\displaystyle
Asymmetric_relation
Mathematical operation
of binary relations, the composition of relations is the forming of a new binary relation R ; S {\displaystyle R\mathbin {;} S} from two given binary relations
Composition_of_relations
Mathematical function such that every output has at least one input
right-unique binary relation between X and Y by identifying it with its function graph. A surjective function with domain X and codomain Y is then a binary relation
Surjective_function
Any one of the distinct objects that make up a set in set theory
conditions of membership for x, is the power set of U such that the binary relation of the membership of x in y is any subset of the cartesian product
Element_of_a_set
Pair of related terms or concepts that are opposite in meaning
term, as in binary code. For instance, 'hot' gains meaning because of its relation to 'cold,' and vice versa. It is not a contradictory relation but a structural
Binary_opposition
Type of residuated Boolean algebra with extra structure
of binary relations R {\displaystyle R} and S {\displaystyle S} , and with the converse of R {\displaystyle R} as the converse relation. Relation algebra
Relation_algebra
Axiom set used in first-order logic
background logic includes identity, a binary relation denoted by =. The axioms below are grouped by the types of relation they invoke, then sorted, first by
Tarski's_axioms
Order whose elements are all comparable
which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies
Total_order
Mathematical relation inside orderings
mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are
Covering_relation
Branch of mathematics
arithmetic, and binary relations. Orders are special binary relations. Suppose that P is a set and that ≤ is a relation on P ('relation on a set' is taken
Order_theory
Type of binary relation
binary relations that formalize "Axiom 1" in Euclid's Elements: "Magnitudes which are equal to the same are equal to each other." A binary relation R
Euclidean_relation
Mapping of mathematical formulas to a particular meaning
elements and an interpretation of the ∈ {\displaystyle \in } relation as a binary relation on these elements. A {\displaystyle {\mathcal {A}}} is called
Structure (mathematical logic)
Structure_(mathematical_logic)
Number expressed in the base-2 numeral system
systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Europe and India, e.g. in relation to divination
Binary_number
Study of the cultural legacy of colonialism and imperialism
identity; and how neocolonialism actively employs the 'us-and-them' binary social relation to view the non-Western world as inhabited by 'the other'. As an
Postcolonialism
Mathematical set with an ordering
every pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered
Partially_ordered_set
Topics referred to by the same term
partial order without incomparable pairs Total relation, which may also mean connected relation (a binary relation in which any two elements are comparable)
Total
Graph with oriented edges
a directed path to every vertex from a distinguished root vertex. Binary relation – Relationship between elements of two sets Coates graph – Mathematical
Directed_graph
Math relation that is reflexive and symmetric
A congruence relation is a tolerance relation that also forms a set partition. Let ∼ {\displaystyle \sim } be a tolerance binary relation on an algebraic
Tolerance_relation
Glossary of terms used in branch of mathematics
0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Acyclic. A binary relation is acyclic if it contains no "cycles": equivalently, its transitive
Glossary_of_order_theory
Generalised alphabetical order
the lexicographical order. For instance, the set of countably infinite binary sequences (by definition, the set of functions from natural numbers to {
Lexicographic_order
Assignment of meaning to the symbols of a formal language
constant symbols 0 and 1, two binary function symbols + and ·, and no binary relation symbols. (Here the equality relation is taken as a logical constant
Interpretation_(logic)
is found to be used for either of these. A binary relation # {\displaystyle \#} is an apartness relation if it satisfies: ¬ ( x # x ) {\displaystyle
Apartness_relation
Formal system for transcribing expressions into equivalent terms
simplest form, an ARS is simply a set (of "objects") together with a binary relation, traditionally denoted with → {\displaystyle \rightarrow } ; this definition
Abstract_rewriting_system
Vertices connected in pairs by edges
graphs are considered, but they are usually viewed as a special kind of binary relation, because most results on finite graphs either do not extend to the
Graph_(discrete_mathematics)
Mathematical concept for comparing objects
equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is
Partial_equivalence_relation
Index of articles associated with the same name
different types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes
Preference_relation
Concept in philosophy and psychology
binary-gender relation that is the Man and Woman relation. The deconstruction of the word Woman (the subordinate party in the Man and Woman relation)
Other_(philosophy)
Branch of mathematics that studies sets
objects, the membership relation can relate sets as well, i.e., sets themselves can be members of other sets. A derived binary relation between two sets is
Set_theory
Cartesian product of two sets is called a binary relation or correspondence; thus, a correspondence here is a relation that is defined by algebraic equations
Correspondence (algebraic geometry)
Correspondence_(algebraic_geometry)
Topics referred to by the same term
Binary function, a function that takes two arguments Binary operation, a mathematical operation that takes two arguments Binary relation, a relation involving
Binary
In mathematics, invertible homomorphism
object consists of a set X with a binary relation R and the other object consists of a set Y with a binary relation S then an isomorphism from X to Y
Isomorphism
Type of infinite structure
model theory. Namely, if L {\displaystyle L} is a language including a binary relation < {\displaystyle <} , and ( M , < , … ) {\displaystyle (M,<,\dots )}
O-minimal_theory
Type of abstract object
binary relation has a converse relation, and the converse of ∈ {\displaystyle \in } is written ∋ {\displaystyle \ni } . Also, a binary relation must have
Domain_of_discourse
Alternative mathematical ordering
binary relation, such as "a < b". One does not say that east is "more clockwise" than west. Instead, a cyclic order is defined as a ternary relation [a
Cyclic_order
Overview of and topical guide to discrete mathematics
formula – Expression for sums of powers Binary relation – Relationship between elements of two sets Heterogeneous relation – Relationship between elements of
Outline of discrete mathematics
Outline_of_discrete_mathematics
Topics referred to by the same term
one element in the Unified Modeling Language Dependency relation, a type of binary relation in mathematics and computer science. Functional dependency
Dependency
Theories in mathematical logic
transcendental. The signature of equivalence relations has one binary infix relation symbol ~, no constants, and no functions. Equivalence relations
List_of_first-order_theories
Function that preserves distinctness
algebraic structures is an embedding. Unlike surjectivity, which is a relation between the graph of a function and its codomain, injectivity is a property
Injective_function
Operation on mathematical functions
as a special case of a binary relation (namely functional relations), function composition satisfies the definition for relation composition. A small circle
Function_composition
Class of mathematical orderings
negative integers does not contain a least element. The following binary relation R is an example of well ordering of the integers: x R y if and only
Well-order
Symbol used in mathematics and logic
similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: Perpendicularity of lines in geometry Orthogonality
Up_tack
Property of elements related by inequalities
respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true. They are called incomparable if they are not comparable. A binary relation on a set
Comparability
Equivalence relation in algebra
single binary operation, satisfying certain axioms. If G {\displaystyle G} is a group with operation ∗ {\displaystyle \ast } , a congruence relation on G
Congruence_relation
Expression whose definition assigns it a unique interpretation
1)\in f} , which makes the binary relation f {\displaystyle f} not functional (as defined in Binary relation § Types of binary relations) and thus not well
Well-defined_expression
Standard system of axiomatic set theory
which is a predicate symbol of arity 2 (a binary relation symbol). This symbol symbolizes a set membership relation. For example, the formula a ∈ b {\displaystyle
Zermelo–Fraenkel_set_theory
Property of a relation on a set
In mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all distinct pairs of elements of the set in
Connected_relation
One-to-one correspondence
of mathematical objects of apparently very different nature. For a binary relation pairing elements of set X with elements of set Y to be a bijection
Bijection
Topics referred to by the same term
Functional relation may refer to A binary relation that is the graph of a function or a partial function An alternative name for a functional equation
Functional_relation
Mathematical property of subsets in order theory
{\displaystyle A.} Let ≤ {\displaystyle \,\leq \,} be a homogeneous binary relation on a set A . {\displaystyle A.} A subset B ⊆ A {\displaystyle B\subseteq
Cofinal_(mathematics)
Process calculus
{\displaystyle a} . A binary relation R {\displaystyle R} over processes is a barbed bisimulation if it is a symmetric relation which satisfies that for
Π-calculus
Reasoning about equations with free variables
(Czelakowski 2003). A homogeneous binary relation is found in the power set of X × X for some set X, while a heterogeneous relation is found in the power set
Algebraic_logic
Partial order with joins
commutative, idempotent binary operations linked by corresponding absorption laws. A set S partially ordered by the binary relation ≤ is a meet-semilattice
Semilattice
Smallest transitive relation containing a given binary relation
mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite
Transitive_closure
Mathematical relation making a non-equal comparison
a strictly increasing function.) A (non-strict) partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive. That
Inequality_(mathematics)
Mathematical ranking of a set
ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible
Weak_ordering
Mathematical result on order relations
form of Zorn's lemma to find a maximal set with certain properties. A binary relation R {\displaystyle R} on a set X {\displaystyle X} is formally defined
Szpilrajn_extension_theorem
Any binary relation equal to its composition with itself
In mathematics, an idempotent binary relation is a binary relation R on a set X (a subset of Cartesian product X × X) for which the composition of relations
Idempotent_relation
Theory of relational databases
tuples (rows) from an input relation. Binary operators accept two relations as input and combine them into a single output relation. For example, taking all
Relational_algebra
Relation between transition systems in computer science
In theoretical computer science, a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way
Bisimulation
Well-quasi-ordering of finite trees
v t e Order theory Topics Glossary Category Key concepts Binary relation Boolean algebra Cyclic order Lattice Partially ordered set Preorder Total order
Kruskal's_tree_theorem
Mathematical model used by graph-oriented databases
u for origin and node v for target κ {\displaystyle \kappa } is a binary relation over (A∪N) and K (formally defined as a subset of the cartesian product
Property_graph
Set-theoretic concept
choice. A weakening of being a Berkeley cardinal is that for every binary relation R on Vκ, there is a nontrivial elementary embedding of (Vκ, R) into
Berkeley_cardinal
Mathematical structure combining Boolean algebra with additional residuation operations
all binary relations on a given set X {\displaystyle X} under relational composition, and more generally the power set of any equivalence relation, again
Residuated_Boolean_algebra
Topics referred to by the same term
a mathematical structure of sets in an abstract space Field of a binary relation, union of its domain and its range Field of view, the area of a view
Field
Creating a model of the data in a system
example, a generic data model may define relation types such as a 'classification relation', being a binary relation between an individual thing and a kind
Data_modeling
Mathematical operation with two operands
a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation
Binary_operation
Concept in order theory
\wedge )} is then a meet-semilattice. Moreover, we then may define a binary relation ≤ {\displaystyle \,\leq \,} on A, by stating that x ≤ y {\displaystyle
Join_and_meet
Mathematical concept
-\sin(\theta )}}}\right)^{n}\right).} Since a function is a special type of binary relation, many of the properties of an inverse function correspond to properties
Inverse_function
Fragment of first-order logic
is logically valid (true for all nonempty domains). Adding a single binary relation symbol to monadic logic, however, results in an undecidable logic.
Monadic_predicate_calculus
introduced by Sen (1969) to study the consequences of Arrow's theorem. A binary relation T over a set X is quasitransitive if for all a, b, and c in X the following
Quasitransitive_relation
elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication
Construction of the real numbers
Construction_of_the_real_numbers
In mathematical logic, the ancestral relation (often shortened to ancestral) of a binary relation R is its transitive closure, however defined in a different
Ancestral_relation
Mathematical proposition equivalent to the axiom of choice
Preliminary notions: Partially ordered set A set P equipped with a binary relation ≤ that is reflexive (x ≤ x for every x), antisymmetric (if both x ≤
Zorn's_lemma
Isomorphism from A to the opposite of B
applied to rings. Let A be the binary relation (or directed graph) consisting of elements {1,2,3} and binary relation → {\displaystyle \rightarrow } defined
Antiisomorphism
mathematics, see glossaries in Category:Glossaries of mathematics. binary A binary relation is a set of ordered pairs; an element x is said to be related to
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Law (all real numbers are positive, negative, or 0)
real number is either positive, negative, or zero. More generally, a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of
Law_of_trichotomy
Symbols requiring interpretation
For example a signature could consist of a binary function symbol +, a constant symbol 0, and a binary relation symbol <. Structures over a signature, also
Non-logical_symbol
Set theory concept
relation. A prewellordering on a set X {\displaystyle X} is a homogeneous binary relation ≤ {\displaystyle \,\leq \,} on X {\displaystyle X} that satisfies the
Prewellordering
BINARY RELATION
BINARY RELATION
Boy/Male
Indian, Punjabi, Sikh
Blessing
Girl/Female
English
Originally a diminutive used for names ending in -bina, like Albina, Columbina, and Robina, now...
Boy/Male
Indian
An intimate particle of the God of heaven
Boy/Male
Latin
Happy; Cheerful.
Girl/Female
Indian
Modesty
Male
Hindi/Indian
Variant spelling of Hindi Vijay, BIJAY means "victory."
Girl/Female
Indian
(the wife of Sage Kashyap)
Female
Hebrew
Variant spelling of Hebrew Bina, BINAH means "intelligence, wisdom."Â
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Surname or Lastname
English (chiefly South Yorkshire)
English (chiefly South Yorkshire) : topographic name for someone who lived on land enclosed by a bend in a river, from Old English binnan ēa ‘within the river’, or a habitational name from places in Kent called Binney and Binny, which have this origin.Scottish : habitational name from Binney or Binniehill near Falkirk, named in Gaelic as Beinnach, from beinn ‘hill’ + the locative suffix -ach.
Surname or Lastname
English
English : variant spelling of Vickery.
Male
English
English unisex form of Latin Hilarius and Hilaria, HILARY means "joyful; happy."Â Originally, this was strictly a masculine name.
Boy/Male
Irish
An ancient Irish name whos meaning is lost in antiquety.
Female
Turkish
Turkish name PINAR means "spring."
Male
Hindi/Indian
(विनय) Hindi name VINAY means "leading asunder."
Female
English
English pet form of German Belinda, possibly BINDY means "bright serpent" or "bright linden tree."
Boy/Male
American, Australian, French, German, Greek, Latin, Polish, Swedish
Cheerful; Happy; Joyful; Similar to Hilary
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Female
Hebrew
(×‘Ö¼Ö´×™× Ö¸×”) Hebrew name BINA means "intelligence, wisdom."Â
BINARY RELATION
BINARY RELATION
Male
English
 Anglicized form of Greek Nachor (Hebrew Nachowr), NAHOR means "snoring" or "snorting." In the bible, this is the name of the son of Terah and brother of Abraham. Compare with another form of Nahor.
Girl/Female
Tamil
Boy/Male
Indian, Tamil
Dust
Boy/Male
Indian
Warrior, A companion, One on expedition, To conquer
Boy/Male
Muslim
Merciful heart
Boy/Male
Arabic
Elegant
Boy/Male
German
Mountain.
Female
English
Anglicized form of Irish Gaelic Eithne, ETHNA means "kernel."
Boy/Male
Hindu
A king from the epic mahabharata
Girl/Female
Hindu, Indian, Marathi
Graceful; Splendid
BINARY RELATION
BINARY RELATION
BINARY RELATION
BINARY RELATION
BINARY RELATION
n.
A binary compound of silicon, or one regarded as binary.
n.
A binary compound of selenium, or a compound regarded as binary; as, ethyl selenide.
n.
A binary compound of iodine, or one which may be regarded as binary; as, potassium iodide.
n.
A binary compound of hydrogen; a hydride.
a.
Of a pale yellowish color; as, Canary stone.
n.
That which is constituted of two figures, things, or parts; two; duality.
n.
See Finery.
v. i.
To perform the canary dance; to move nimbly; to caper.
a.
Of or pertaining to the Canary Islands; as, canary wine; canary birds.
n.
Wine made in the Canary Islands; sack.
n.
A binary compound of zinc.
a.
Of or pertaining to the urine; as, the urinary bladder; urinary excretions.
n.
A register of daily events or transactions; a daily record; a journal; a blank book dated for the record of daily memoranda; as, a diary of the weather; a physician's diary.
a.
Containing ten; tenfold; proceeding by tens; as, the denary, or decimal, scale.
n.
A canary bird.
a.
Relating or belonging to bile; conveying bile; as, biliary acids; biliary ducts.
n.
A binary compound of phosphorus.
n.
A pale yellow color, like that of a canary bird.
a.
lasting for one day; as, a diary fever.
a.
Compounded or consisting of two things or parts; characterized by two (things).