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Q: The set of rational and irrational numbers?

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It is the set of Real numbers.

The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.

The intersection between rational and irrational numbers is the empty set (Ø) since no rational number (x∈ℚ) is also an irrational number (x∉ℚ)

The real number system

No. The set of irrational numbers has the same cardinality as the set of real numbers, and so is uncountable.The set of rational numbers is countably infinite.

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The Real numbers

No, a number is either rational or irrational

It is the set of Real numbers.

real numbers

The real numbers.

Are in the set of real numbers.

The set of real numbers.

There is no representation for irrational numbers: they are represented as real numbers that are not rational. The set of real numbers is R and set of rational numbers is Q so that the set of irrational numbers is the complement if Q in R.

No. Irrational and rational numbers can be non-negative.

The set of Real numbers.

The real numbers.

Yes. The rational numbers are countable, that is they can be put in a one-to-one correspondence with the counting numbers, but the irrational numbers cannot and so are not countable. There is a higher infinity of irrational numbers than the infinity of rational numbers.

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