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Binary relation

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 codomain. Precisely, a binary relation over sets X {\displaystyle X} and Y {\displaystyle Y} is a set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where x {\displaystyle x} is an element of X…

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Overview

Definition

Operations

Examples

Types of binary relations

Sets versus classes

Homogeneous relation

Calculus of relations

Induced concept lattice

Particular relations

Preorder R\R

Fringe of a relation

Mathematical heaps

Bibliography

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Binary relation

Nodes183
Edges182
Triples108
Avg. degree1.99
Density0.010929
Components1

How this topic connects Entity context

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Binary relation

Top relations

related to Examples · 41
Binary relation → AA, AF, An, Arctic, As, Atlantic, AU, Australia, But, Earth, EU, Europe, Finite, For, He, Hermann Minkowski, Hyperbolic, Ian, Indian, Jakob Steiner
related to Sets versus classes · 8
Binary relation → Also, Bertrand Russell, Certain, For, In, Russell's, Similarly, The
related to Calculus of relations · 7
Binary relation → But, Developments, In, Nevertheless, Rel, Schröder, The
related to Mathematical heaps · 7
Binary relation → Christopher Hollings, Given, In, Iron Curtain, Mathematics, The, Viktor Wagner
related to Ferrers type · 6
Binary relation → Ferrer's, Ferrers, In, Jacques Riguet, The, Thus
related to Matrix representation · 6
Binary relation → AND, Binary, Boolean, Hadamard, Homogeneous, OR
related to Homogeneous relation · 5
Binary relation → Boolean, Cartesian, Considering, It, The
related to Definition · 4
Binary relation → Cartesian, Given, In, The
related to External links · 4
Binary relation → Binary, EMS Press, Encyclopedia, Mathematics
related to Induced concept lattice · 3
Binary relation → Binary, The, Thus

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Important terminology

displaystyle relation binary relations set example sets called one also xry codomain homogeneous subset total subseteq times element diagram domain

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Binary relationis amost studied special case n0.90text
Russell's paradox.A binary relation is the most studied special case ninstance ofwithout running into logical inconsistencies0.80text
Binary relationrelated to Calculus of relationsDevelopments0.60section
Binary relationrelated to Calculus of relationsThe0.60section
Binary relationrelated to Calculus of relationsBut0.60section
Binary relationrelated to Calculus of relationsNevertheless0.60section
Binary relationrelated to Calculus of relationsSchröder0.60section
Binary relationrelated to Calculus of relationsIn0.60section
Binary relationrelated to Calculus of relationsRel0.60section
Binary relationrelated to ComplementIf0.60section
Binary relationrelated to ComplementFor0.60section
Binary relationrelated to CompositionIf0.60section

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