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Subjects>Math>Math & Arithmetic

How do you prove the set of rational numbers are uncountable?

Anonymous

∙ 10y ago

Updated: 11/4/2022

They are not. They are countably infinite. That is, there is a one-to-one mapping between the set of rational numbers and the set of counting numbers.

Wiki User

∙ 10y ago

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Q: How do you prove the set of rational numbers are uncountable?

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Are most numbers rational or irrational?

The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.

Are integers in a set of rational numbers?

Yes - the set of integers is a subset of the set of rational numbers.

Is the set of rational numbers finite?

No; there are infinitely many rational numbers.

How are rational number different from fractional and whole number?

The set of rational numbers is the union of the set of fractional numbers and the set of whole numbers.

Is the set of rational numbers is larger than the set of integers?

Yes, rational numbers are larger than integer because integers are part of rational numbers.

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