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No.
4 root 2 and 2 root 2 are both irrational. Divide the first by the second you get 2.
Which is not a member of the set of Irrational Numbers.
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Is the set of irrational numbers closed under subtraction?
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.
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
Is the set of rational numbers closed under division and Why?
No. Zero is a rational number, but division by zero is not defined.
Are irrational numbers closed under multiplication?
No. To say a set is closed under multiplication means that if you multiply any two numbers in the set, the result is always a member of the set. If, say, the 2 numbers are radical 2 and radical 2 we have (1.4142...)(1.4142...) which by definition equals 2. The result is not an irrational number, so the set is not closed.
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.
Is the set of irrational numbers closed under division?
No, it is not. Root2 and root 8 are each irrational. Root8 / root2 =2. 2 is not a member of the set.
What operations are irrational numbers closed under?
None.
Is the set of irrational numbers closed under addition?
no it is not
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.
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 subtraction?
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.
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
Is irrational numbers closed under division?
Nope. Quick example: e (2.71828) is irrational. Therefore 2*e is irrational making both of them elements of the set of irrational numbers. However, dividing the two, e/(2*e), gives you 1/2, which is a rational number.
Are rational numbers closed under division?
No.
Are real numbers closed under division?
no
What set of numbers is closed under division?
Integers are closed under division I think o.o. It's either counting numbers, integers or whole numbers . I cant remember :/
