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Why is division not closed for rational numbers give an example?
Wiki User
∙ 8y ago
If a set is closed under an operation. then the answer will be a part of that set.
If you add, subtract or multiply any two rational numbers you get another national number.
But when it comes to division, it is closed except for one number and that is ZERO.
eg 3.56 (rational number) ÷ 0 = no answer.
Since no answer is not a rational number, that rational numbers are not closed under the operation of division.
Wiki User
∙ 8y ago
Wiki User
∙ 8y ago0 is a rational number but division by 0 is not defined.
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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 the set of rational numbers closed under division?
No, it is not. Division by zero (a rational) is not defined.
What is an example of whole numbers are closed under division?
The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.
What binary operations have closure?
Closure depends on the set as much as it depends on the operation.For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.The set {1, 2, 3} is not closed under addition.
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
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 the set of rational numbers closed under division?
No, it is not. Division by zero (a rational) is not defined.
Are rational numbers closed under division?
No.
Is the set of rational numbers closed under division and Why?
No. Zero is a rational number, but division by zero is not defined.
Why are rational numbers not like integers?
The set of rational numbers is closed under division, the set of integers is not.
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 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 closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
What does this mean Which set of these numbers is closed under division?
It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.
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.
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
