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What does commutative mean?

Definitions for commutative
kəˈmyu tə tɪv, ˈkɒm yəˌteɪ tɪvcom·mu·ta·tive

This dictionary definitions page includes all the possible meanings, example usage and translations of the word commutative.

Princeton's WordNet

  1. commutativeadjective

    (of a binary operation) independent of order; as in e.g. "a x b = b x a"

GCIDE

  1. Commutativeadjective

    (Math.) having the property of commutativity.

Wiktionary

  1. commutativeadjective

    Such that the order in which the operands are taken does not affect their image under the operation.

    Addition on the real numbers is commutative because for any real numbers uE00097754uE001, uE00097755uE001.

  2. commutativeadjective

    Having a commutative operation.

  3. commutativeadjective

    Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.

Samuel Johnson's Dictionary

  1. Commutativeadjective

    Relative to exchange; as commutative justice, that honesty which is exercised in traffick, and which is contrary to fraud in bargains.

    Etymology: from commute.

Wikipedia

  1. commutative

    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 something like "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, and so are referred to as noncommutative operations. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is symmetric as two equal mathematical objects are equal regardless of their order.

ChatGPT

  1. commutative

    Commutative refers to a property in mathematics where the order in which two numbers or quantities are combined does not affect the result. This is most commonly applicable in addition and multiplication. For example, 2+3 is the same as 3+2, and 2*3 is the same as 3*2. This condition does not hold for all operations, such as subtraction or division.

Webster Dictionary

  1. Commutativeadjective

    relative to exchange; interchangeable; reciprocal

  2. Etymology: [CF. F. commutatif.]

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Numerology

  1. Chaldean Numerology

    The numerical value of commutative in Chaldean Numerology is: 9

  2. Pythagorean Numerology

    The numerical value of commutative in Pythagorean Numerology is: 7

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"commutative." Definitions.net. STANDS4 LLC, 2024. Web. 16 Apr. 2024. <https://www.definitions.net/definition/commutative>.

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