yes
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No, it is not.
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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)
no
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.