Yes.
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Yes it is : a + b = b + a for all integers a and b. In fact , if an operation is called addition you can bet that it is commutative. It would be perverse to call an non-commutative operation addition.
The commutative property of addition and the commutative property of multiplication.
There are infinitely many of them. Amongst unary functions, there are squares, cubes and other powers and their combinations - that is polynomials. There are trigonometric functions, power functions, reciprocals and so on. Then there are binary functions such as addition, subtraction, multiplication, division and also variable powers.
Yes. The commutative property of addition (as well as the commutative property of multiplication) applies to all real numbers, and even to complex numbers. As an example (for integers): 5 + (-3) = (-3) + 5
Commutative Law: a + b = b + a Associative Law: (a + b) + c = a + (b + c)