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Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is numerical equality. Any number a {\displaystyle a} is equal to itself (reflexive). If a = b {\displaystyle a=b} , then b…

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Connections to other relations

Partial orderAntisymmetricEqualityAlgebraic expressionsSubstituted
21 related topics

Algebraic structure

Order relationsLatticesGroup theoryCategoriesGroupoid
30 related topics

Examples

SimilarTrianglesCongruentFunctionImage
13 related topics

Generating equivalence relations

Fixed pointsCardinalitySurjectivePreimagesSingletons
12 related topics

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Well-definedness under an equivalence relation

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Comparing equivalence relations

Generating equivalence relations

Algebraic structure

Equivalence relations and mathematical logic

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Equivalence relation

Nodes120
Edges119
Triples147
Avg. degree1.98
Density0.016667
Components1

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Equivalence relation

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related to References · 50
Equivalence relation → Algebraic Theory, Axioms, Booksurge LLC, Brading, Brown, Cambridge Univ, Castellani, Categories, Chapter, Chpt, Crawley, Downloadable, Foundations, Founded, Groupoids, Higgins, How Science, Introduction, ISBN, John Randolph Lucas
related to Generating equivalence relations · 12
Equivalence relation → An, Cartesian, Concretely, Conversely, Equivalence, Given, Let, The, Then, This, Thus, Two
related to External links · 10
Equivalence relation → Accessed, Binary, Bogomolny, EMS Press, Encyclopedia, Equivalence, Equivalence Relationship, Mathematics, PlanetMathOEISsequenceA231428, September
related to Connections to other relations · 8
Equivalence relation → Any, Each, Equality, Euclidean, In, Such, The, Therefore
related to Equivalence relations · 7
Equivalence relation → For, Given, Has, Have, In, Is, The
see also · 7
Equivalence relation → Borel, Concept, Generalization, Graph, In, Mathematical, Property
related to Alternative definition using relational algebra · 6
Equivalence relation → Here, In, RR, SR, The, This
related to Group theory · 5
Equivalence relation → Hence, Just, Let, Since, Then
related to Well-definedness under an equivalence relation · 5
Equivalence relation → If, See, Some, The, This
is a · 4
Equivalence relation → binary relation that is reflexive, finest equivalence relation on any set, negation of an apartness relation, ternary analogue to the usual

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Important terminology

equivalence relation displaystyle set sim relations partition reflexive transitive classes class symmetric elements also defined group function structure example theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Equivalence relationis abinary relation that is reflexive0.90text
Equivalence relationis aternary analogue to the usual0.90text
Equivalence relationis anegation of an apartness relation0.90text
Equivalence relationis afinest equivalence relation on any set0.90text
Equivalence relationrelated to Algebraic structureMuch0.60section
Equivalence relationrelated to Algebraic structureLattice0.60section
Equivalence relationrelated to Algebraic structureEven0.60section
Equivalence relationrelated to Algebraic structureThe0.60section
Equivalence relationrelated to Alternative definition using relational algebraIn0.60section
Equivalence relationrelated to Alternative definition using relational algebraSR0.60section
Equivalence relationrelated to Alternative definition using relational algebraThis0.60section
Equivalence relationrelated to Alternative definition using relational algebraThe0.60section

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