No, they are not. An irrational number subtracted from itself will give 0, which is rational.
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Irrational numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, under division.
A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .
no it is not
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Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.