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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 addition?
no it is not
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
Are irrational numbers closed under subtraction?
No, they are not. An irrational number subtracted from itself will give 0, which is rational.
Can you add two rational numbers and get an irrational number?
No. The set of rational numbers is closed under addition (and multiplication).
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 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.
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.
When is a set of negative irrational numbers closed?
It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.
Are a set of irrational numbers closed under exponents?
No. Sqrt (2) is irrational. Square it, or raise it to any even power, and it becomes rational. The set is not closed under exponentiation.
Are whole numbers closed under the operations of multiplication?
Yes.
What answer choice shows that the set of irrational numbers is not closed under addition?
Hennd
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
Are irrational numbers closed under subtraction?
No, they are not. An irrational number subtracted from itself will give 0, which is rational.
Are irrational numbers closed 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.
Is this set of negative numbers closed under multiplication or addition?
Yes. The empty set is closed under the two operations.
