Commutative property

A binary operation is commutative when swapping its two operands leaves the result unchanged, as in addition: a + b = b + a.

Binary operation: A rule that combines two elements of a set to produce an element. Commutativity is a condition on the output of a binary operation when its inputs are swapped.
Addition: An arithmetic operation that combines quantities into a sum. Ordinary number addition is the standard example: changing addend order preserves the sum.
Associative property: A property stating that regrouping operands does not change the result of an operation. Associativity changes grouping, whereas commutativity changes operand order.
Ring (mathematics): An algebraic structure with addition and multiplication satisfying specified group and distributive laws. Ring addition is commutative, while ring multiplication need not be.
Operand: A quantity or object on which an operation acts. The property compares the result formed from two operands in either order.
Multiplication: An operation that combines quantities into a product. Ordinary multiplication of numbers is commutative, unlike some other products.
Distributive property: A law connecting two operations, such as multiplication distributing over addition. Distributivity relates operations rather than asserting that one operation tolerates swapped operands.
Field (mathematics): A structure in which addition, subtraction, multiplication, and division by nonzero elements obey field axioms. Both addition and multiplication in a field are commutative.
Equality: A relation stating that two expressions have the same value or denote the same object. The defining equation asserts that both operand orders give equal results.
Subtraction: An arithmetic operation that finds the difference between quantities. Reversing minuend and subtrahend usually changes the result, showing the property can fail.

Linked from 12 pages