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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 ...
The community property concept originated in civil law jurisdictions but is now also found in some common law jurisdictions. U.S. states with community property laws draw primarily from the marital property laws under the civil law of France and Spain. [10] Division of community property may take place by item by splitting all items or by values.
Community property (United States) also called community of property (South Africa) is a marital property regime whereby property acquired during a marriage is considered to be owned by both spouses and subject to division between them in the event of divorce. Conversely, property owned by one spouse before the marriage, along with gifts and ...
The commutator of two elements, g and h, of a group G, is the element. [g, h] = g−1h−1gh. This element is equal to the group's identity if and only if g and h commute (that is, if and only if gh = hg ). The set of all commutators of a group is not in general closed under the group operation, but the subgroup of G generated by all ...
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures ...
Greatest common divisor. In mathematics, the greatest common divisor ( GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. [ 1][ 2]
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