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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced…

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Examples

MultiplicationNumber systemsNatural numbersIntegersRational numbers
25 related topics

History and etymology

EgyptiansProductsEuclidElementsFrançois Servois
7 related topics

Commutative structures

Commutative semigroupSemigroupCommutative monoidMonoidAbelian group
10 related topics

Definition

Set
1 related topics

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Field
Algebra
Statement
A binary operation is commutative if changing the order of the operands does not change the result.
Symbolic statement
x ∗ y = y ∗ x ∀ x , y ∈ S . {\displaystyle x*y=y*x\quad \forall x,y\in S.}
Type
Property

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Overview

Definition

  • Set Set (mathematics)

Examples

Commutative structures

History and etymology

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Commutative property

Nodes58
Edges57
Triples26
Avg. degree1.97
Density0.034483
Components1

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Commutative property

Top relations

related to history · 16
Commutative property → Commutative, Duncan Gregory's, Edinburgh, Elements, English, Euclid, Formal, François Servois, French, Nowadays, On, Records, Royal Society, The, The Egyptians, Transactions
see also · 5
Commutative property → Anticommutative, Centralizer, Commutative, CommutatorCommuting, Quasi-commutative
Field · 1
Commutative property → Algebra
Statement · 1
Commutative property → A binary operation is commutative if changing the order of the operands does not change the result.
Symbolic statement · 1
Commutative property → x ∗ y = y ∗ x ∀ x , y ∈ S . {\displaystyle x*y=y*x\quad \forall x,y\in S.}
Type · 1
Commutative property → Property
is a · 1
Commutative property → well-known and basic property used in most branches of mathematics.The first recorded use of the term commutative was in a memoir by François Servois in 1814

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Important terminology

commutative property displaystyle operation noncommutative multiplication operations binary operands addition since algebra also elements neq used example structures order commute

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Commutative propertyFieldAlgebra1.00infobox
Commutative propertyStatementA binary operation is commutative if changing the order of the operands does not change the result.1.00infobox
Commutative propertySymbolic statementx ∗ y = y ∗ x ∀ x , y ∈ S . {\displaystyle x*y=y*x\quad \forall x,y\in S.}1.00infobox
Commutative propertyTypeProperty1.00infobox
Commutative propertyis awell-known and basic property used in most branches of mathematics.The first recorded use of the term commutative was in a memoir by François Servois in 18140.90text
Commutative propertyrelated to historyRecords0.60section
Commutative propertyrelated to historyThe Egyptians0.60section
Commutative propertyrelated to historyEuclid0.60section
Commutative propertyrelated to historyElements0.60section
Commutative propertyrelated to historyFormal0.60section
Commutative propertyrelated to historyNowadays0.60section
Commutative propertyrelated to historyThe0.60section

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