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No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction:

pi - pi = 0.

pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of Irrational Numbers is NOT closed under subtraction.

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Q: Is the set of irrational numbers closed under subtraction?
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