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# Is the set of irrational numbers closed under subtraction?

Wiki User

2009-06-30 20:16:14

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.

Wiki User

2009-06-30 20:16:14
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