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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 an irrational number closed under division?
No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
Which answer choice shows that the set of irrational numbers is not closed under addition?
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.
Is this set of negative numbers closed under multiplication or addition?
Yes. The empty set is closed under the two operations.
Are whole numbers closed under the operations of multiplication?
Yes.
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.
What operations are irrational numbers closed under?
None.
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.
Is the set of irrational numbers closed under addition?
no it is not
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.
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 irrational numbers closed under subtraction?
No, they are not. An irrational number subtracted from itself will give 0, which is rational.
Is an irrational number closed under division?
No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
What answer choice shows that the set of irrational numbers is not closed under addition?
Hennd
Which answer choice shows that the set of irrational numbers is not closed under addition?
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.
Are irrational numbers closed under addition?
No. For example, the sum of pi and -pi is zero, which is rational - while each of the addends is irrational.
