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Q: What answer choice shows that the set of irrational numbers is not closed under addition?
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What do rational and irrational numbers have in common?

Rational and irrational numbers are part of the set of real numbers. There are an infinite number of rational numbers and an infinite number of irrational numbers. But rational numbers are countable infinite, while irrational are uncountable. You can search for these terms for more information. Basically, countable means that you could arrange them in such a way as to count each and every one (though you'd never count them all since there is an infinite number of them). I guess another similarity is: the set of rational numbers is closed for addition and subtraction; the set of irrational numbers is closed for addition and subtraction.


When is a set of negative irrational numbers closed?

It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.


What is closed and not-closed under addition?

The set of even numbers is closed under addition, the set of odd numbers is not.


Why are odd integers closed under multiplication but not under addition?

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.


Are real numbers closed under addition?

yes because real numbers are any number ever made and they can be closed under addition

Related questions

Is the set of irrational numbers closed under addition?

no it is not


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.


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.


Is the set of irrational numbers closed for addition?

No. Sqrt(2) is irrational, as is -sqrt(2). Both belong to the irrationals but their sum, 0, is rational.


What do rational and irrational numbers have in common?

Rational and irrational numbers are part of the set of real numbers. There are an infinite number of rational numbers and an infinite number of irrational numbers. But rational numbers are countable infinite, while irrational are uncountable. You can search for these terms for more information. Basically, countable means that you could arrange them in such a way as to count each and every one (though you'd never count them all since there is an infinite number of them). I guess another similarity is: the set of rational numbers is closed for addition and subtraction; the set of irrational numbers is closed for addition and subtraction.


Are irrational addition numbers closed under the closure property?

No. For example, the square root of two plus (minus the square root of two) = 0, which is not an irrational number.


How real numbers are divided into subgroups?

The main subgroup is the rational numbers. The set of irrational numbers is not closed with regard to addition basic arithmetical operations and so does not form a group.


Is the set of irrational numbers closed under mulriplication?

No. You can well multiply two irrational numbers and get a result that is not an irrational number.


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.


When is a set of negative irrational numbers closed?

It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.


What is closed and not-closed under addition?

The set of even numbers is closed under addition, the set of odd numbers is not.