COMMUTATIVE Meaning and
Definition
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The term "commutative" is an adjective that describes a mathematical property or operation where the order of the elements does not affect the result. It is derived from the Latin word "commutare" meaning "to exchange" or "to replace."
In mathematics, commutativity refers to the property of an operation that allows the elements being operated on to be rearranged without changing the outcome. For example, in basic arithmetic, the commutative property of addition states that when adding two numbers, the order of the numbers does not matter. This means that a + b will always yield the same result as b + a.
The commutative property is often associated with binary operations, where two elements are combined to produce a third element. Common examples of commutative operations include addition, multiplication, and bitwise operations like XNOR. Conversely, operations like subtraction and division are non-commutative, as changing the order of the elements results in different outcomes.
The concept of commutativity extends to various branches of mathematics, including abstract algebra, group theory, and linear algebra. It is a fundamental property that enables the simplification and analysis of mathematical expressions and structures. The lack of commutativity in certain operations and structures can have profound consequences and significantly impact their properties and behavior.
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Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
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Etymology of COMMUTATIVE
The word commutative comes from the Latin word commutare, which means to change or to exchange. It is derived from the prefix com, meaning together, and mutare, meaning to change.
Similar spelling words for COMMUTATIVE
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