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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).
What operations are irrational numbers closed under?
None.
Is the set of irrational numbers closed under addition?
no it is not
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.
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).
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.
Is the set of irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Are the prime numbers closed under multiplication?
No.
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.
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.
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.
Why are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Are the rational numbers closed under multiplication?
Yes.
