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Subjects>Math>Algebra

Are set of irrational number closed under addition?

Anonymous

∙ 12y ago

Updated: 11/18/2024

No. 2 + sqrt(5) and 2 - sqrt(2) are both irrational but their sum, 4 is rational.

Wiki User

∙ 8y ago

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Q: Are set of irrational number closed under addition?

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Continue Learning about Algebra

Is the set of irrational numbers closed under addition?

no it is not

Can you add two rational numbers and get an irrational number?

No. The set of rational numbers is closed under addition (and multiplication).

Are irrational numbers closed under addition?

No. For example, the sum of pi and -pi is zero, which is rational - while each of the addends is irrational.

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.

Which of the following is an example of why irrational numbers are not closed under addition?

Don't know about the "following" but any irrational added to its additive inverse is 0, which is rational. Therefore, the set of irrationals is not closed under addition.

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