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Under what operation is the set of positive rational numbers not closed?
Subtraction.
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.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
How do you know that the sum of (-2 34) and 59 rational?
Because both of those numbers are rational. The sum of any two rational numbers is rational.
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 rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
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.
Are rational numbers closed under subtraction operation?
Yes, they are.
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.
Under what operation is the set of positive rational numbers not closed?
Subtraction.
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
Are rational numbers under addition a group?
Yes.
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.
Is the set of integers closed under subtraction?
yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.
What is closing a rational number under addition And can you close them under subtraction multiplication and division?
Rational numbers are numbers that can be expressed as a fraction a/b where a and b are both integers and b is not equal to zero. All integers n are rational numbers because they can be expressed as the fraction n/1. Rational numbers are closed under addition, subtraction, multiplication and division by a non-zero rational. To be closed under addition, subtraction, multiplication and division by a non-zero rational means that if you have two rational numbers, when you add, subtract, multiple or divide them, you will get another rational number. For example, take the rationals 1/3 and 4/3. When you add them together, you get another rational number, 5/3. Same with the other operations. 1/3 - 4/3 = -1 (remember integers are rational, too) (1/3) * (4/3) = 4/9 (1/3) / (4/3) = 1/4
Is the set of rational numbers a commutative group under the operation of division?
No, it is not.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
