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Subjects>Math>Math & Arithmetic

Are the set of rational numbers closed under division?

Anonymous

∙ 10y ago

Updated: 9/24/2023

No, it is not. Division by zero (a rational) is not defined.

Wiki User

∙ 8y ago

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Q: Are the set of rational numbers closed under 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.

Why is division not closed for rational numbers give an example?

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.

Is a rational number closed under addition?

No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.

Are rational numbers closed under addition?

Yes.

Are the rational numbers closed under multiplication?

Yes.

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