No, it is not.
Root2 and root 8 are each irrational. Root8 / root2 =2.
2 is not a member of the set.
No. You can well multiply two irrational numbers and get a result that is not an irrational number.
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.
no
The set of irrational numbers is not closed under addition because there exist two irrational numbers whose sum is a rational number. For example, if we take the irrational numbers ( \sqrt{2} ) and ( -\sqrt{2} ), their sum is ( \sqrt{2} + (-\sqrt{2}) = 0 ), which is a rational number. This demonstrates that adding certain irrational numbers can result in a rational number, confirming that the set is not closed under addition.
The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.
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.
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.
no it is not
None.
No. You can well multiply two irrational numbers and get a result that is not an irrational number.
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.
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.
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
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.
No.
no
Integers are closed under division I think o.o. It's either counting numbers, integers or whole numbers . I cant remember :/