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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.
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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
