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. Most familiar as the name of the property that says "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, "3 − 5 ≠ 5 − 3"), such operations are not commutative, or noncommutative operations. The idea that simple operations, such as multiplication and addition of numbers, are commutative was for many years implicitly assumed and the property was not named until the 19th century when mathematics started to become formalized. A
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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. Most familiar as the name of the property that says "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, "3 − 5 ≠ 5 − 3"), such operations are not commutative, or noncommutative operations. The idea that simple operations, such as multiplication and addition of numbers, are commutative was for many years implicitly assumed and the property was not named until the 19th century when mathematics started to become formalized. A
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25بك المحتوى هنا ينقصه الاستشه ...... ة في العديد من فروع الرياضيات.
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Das Kommutativgesetz (lat. com ...... undlegende Regeln der Algebra.
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De term "commutatief" wordt in ...... le elementen van D commuteren.
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Em matemática, comutatividade ...... s, como a subtração e divisão.
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En matemáticas, la propiedad c ...... n el orden en que se ejecuten.
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En mathématiques, et plus préc ...... ue, pour tous x et y dans S, .
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In matematica, un'operazione b ...... elementi di commutano sempre.
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In mathematics, a binary opera ...... dless of the order of the two.
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Przemienność – jedna z własnoś ...... e liczb nie jest przemienne: .
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Коммутативная операция — бинар ...... льцо называется коммутативным.
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Examples of non-commutative operations
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25بك المحتوى هنا ينقصه الاستشه ...... ة في العديد من فروع الرياضيات.
@ar
Das Kommutativgesetz (lat. com ...... undlegende Regeln der Algebra.
@de
De term "commutatief" wordt in ...... , of symmetrisch, genoemd als:
@nl
Em matemática, comutatividade ...... s, como a subtração e divisão.
@pt
En matemáticas, la propiedad c ...... actores no altera el producto.
@es
En mathématiques, et plus préc ...... ue, pour tous x et y dans S, .
@fr
In matematica, un'operazione b ...... elementi di commutano sempre.
@it
In mathematics, a binary opera ...... arted to become formalized. A
@en
Przemienność – jedna z własnoś ...... e liczb nie jest przemienne: .
@pl
Коммутативная операция — бинар ...... льцо называется коммутативным.
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Commutative property
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Commutativiteit
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Commutatività
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Comutatividade
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Conmutatividad
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Kommutativgesetz
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Loi commutative
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Przemienność
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Коммутативная операция
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عملية تبديلية
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