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Subjects>Math>Math & Arithmetic

Do rational numbers have the density property?

Anonymous

∙ 9y ago

Updated: 9/25/2023

Yes. They are infinitely dense. That is, there are infinitely many rational number between any two numbers.

Wiki User

∙ 8y ago

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Q: Do rational numbers have the density property?

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What is the states that an infinite number of rational numbers can be found between any two rational numbers?

That is the property of infinite density of rational numbers. If x and y are any two rational numbers then w = (x + y)/2 is a rational number between them. And then there is a rational number between x and w. This process can be continued without end.

Is there commutative property of subtraction for rational numbers?

No, there is not.

Which property would be useful in proving that the product of two rational numbers is always rational?

The fact that the set of rational numbers is a mathematical Group.

Which of the following sets of numbers contains multiplicative inverses for all its nonzero elements?

Please don't write "the following" if you don't provide a list. This is the situation for some common number sets:* Whole numbers / integers do NOT have this property. * Rational numbers DO have this property. * Real numbers DO have this property. * Complex numbers DO have this property. * The set of non-negative rational numbers, as well as the set of non-negative real numbers, DO have this property.

What rational numbers are real numbers?

All rational numbers are real numbers.

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