The basic operations are addition (+), subtraction (-), multilpication (*) and division (/).
But there are many others, for example, powers and roots, trigonometric functions, exponents and logarithms.
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The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)
Division, since you can't divide by zero.
Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.
Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.
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