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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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โˆ™ 2009-06-30 20:16:14
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Q: Is the set of irrational numbers closed under subtraction?
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Related questions

What are irrational numbers closed under?

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.


Are irrational numbers closed under subtraction?

No, they are not. An irrational number subtracted from itself will give 0, which is rational.


Are rational numbers closed under subtraction?

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.


Which set of numbers is closed under subtraction?

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .


Are rational numbers closed under division multiplication addition or subtraction?

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.


Is the set of irrational numbers closed under addition?

no it is not


What operations are irrational numbers closed under?

None.


Are rational numbers closed under subtraction operation?

Yes, they are.


Is the set of irrational numbers closed under mulriplication?

No. You can well multiply two irrational numbers and get a result that is not an irrational number.


Which sets of numbers are closed under subtraction?

To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.


Are real numbers closed under addition and subtraction?

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.


Under what operation is the set of positive rational numbers not closed?

Subtraction.

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