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No. We go with the proof of a counter-example. pi is a well known irrational number. So is 1/pi. Then pi x (1/pi) = 1, a rational number. If you're not convinced that 1/pi is irrational as well, assume that 1/pi is rational, so that 1/pi = p/q, where p and q are integers and q is not 0 (implicitly, p is also not 0). Then pi = q/p, a contradiction to the fact that pi is not a rational number.
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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.
Can you add two rational numbers and get an irrational number?
No. The set of rational numbers is closed under addition (and multiplication).
Is the set of irrational numbers closed under addition?
no it is not
What operations are irrational numbers closed under?
None.
Is Natural numbers are closed under multiplication?
Yes.natural numbers are closed under multiplication.It means when the operation is done with natural numbers in multiplication the sum of two numbers is always the natural number.
