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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.
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Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Is natural numbers a closed set under subtraction?
No.A set is closed under subtraction if when you subtract any two numbers in the set, the answer is always a member of the set.The natural numbers are 1,2,3,4, ... If you subtract 5 from 3 the answer is -2 which is not a natural number.
Is the sum of rational numbers always rational?
Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.
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.
Are prime numbers closed under subtraction?
No.
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.
Are irrational numbers closed under subtraction?
No, they are not. An irrational number subtracted from itself will give 0, which is rational.
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Which set of numbers is closed under subtraction?
A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .
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.
Which sets of numbers are closed under subtraction?
To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.
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.
Are rational numbers closed under subtraction operation?
Yes, they are.
Are real numbers closed under addition and subtraction?
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
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.
