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What numbers are The union of the rational and irrational numbers?
The real numbers.
Why is every rational number a real number?
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.
Family tree 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.
Which is not included in the set of rational numbers?
All irrational numbers, complex number and so on.
What is the differences among integers rational numbers real numbers and irrational numbers?
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.
