A property of an operation where changing the order of the operands does not change the result. Addition and multiplication are commutative: a + b = b + a and a × b = b × a.
From Latin 'commutare' meaning to change or exchange, from 'com-' (together) and 'mutare' (to change). The mathematical term was introduced in the 19th century as mathematicians began to systematically study the properties of operations and algebraic structures.
The commutative property reflects a deep truth about certain mathematical operations - they represent processes where order doesn't matter, like combining collections or scaling areas! Interestingly, not all operations are commutative (subtraction and division aren't), and discovering non-commutative algebras in the 19th century opened entirely new branches of mathematics.
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