单词	commutative
释义	commutative adjective com·​mu·​ta·​tive kə-ˈmyü-tə-tiv  ˈkäm-yə-ˌtā-tiv  1 : of, relating to, or showing commutation 2 : of, relating to, having, or being the property that a given mathematical operation and set have when the result obtained using any two elements of the set with the operation does not differ with the order in which the elements are used a commutative group addition of the positive integers is commutative Example Sentences Recent Examples on the Web Addition of ordinary numbers is commutative, as is multiplication, and this is very helpful for simplifying computations. Eugenia Cheng, WSJ, 30 June 2022 Like the quaternions, octonion multiplication is not commutative. Quanta Magazine, 25 Oct. 2018 The elements of class groups must obey the associative and commutative properties of addition, and must include a zero element, such that zero plus any other element leaves the element unchanged. Kevin Hartnett, Quanta Magazine, 2 Mar. 2017 Notice this means that, unlike with the real and complex numbers, multiplication of quaternions is not commutative. Quanta Magazine, 25 Oct. 2018 Word History First Known Use 1612, in the meaning defined at sense 1 Kids Definition commutative adjective com·​mu·​ta·​tive ˈkä-myə-ˌtā-tiv  : being a property of a mathematical operation (as addition or multiplication) in which the result does not depend on the order of the elements The commutative property of addition states that 1 + 2 and 2 + 1 will both have a sum of 3.
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