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Q: A set of numbers combining rational and irrational numbers?

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The real numbers.

There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.

All irrational numbers, complex number and so on.

Integers are whole numbers. They are the counting numbers, 0 and the corresponding negative numbers. Rational numbers are numbers that can be expressed as a ratio of two integers (the second one being non-zero). Irrational numbers are numbers that are not rational numbers. Rational and irrational number together form the set of real numbers.

Start with the set of Natural numbers = N.Combine these with negative natural numbers and you get the set of Integers = Z.Combine these with ratios of two integers, the second of which is positive, and you get the set of Rational numbers = Q.Start afresh with numbers which are not rational, nor the roots of finite polynomial equations. This is the set of transcendental numbers.Combine these with the non-rational roots of finite polynomial equations and you have the set of irrational numbers.Combine the rational and irrational numbers and you have the set of Real numbers, R.

Related questions

No, a number is either rational or irrational

It is the set of Real numbers.

The real numbers.

ratio numbers

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.

The set of real numbers.

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

No. Although there are infinitely many of either, there are more irrational numbers than rational numbers. The cardinality of the set of rational numbers is Ã€0 (Aleph-null) while the cardinality of the set of irrational numbers is 2Ã€0.

The set of Real numbers.

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 numbers.