The set of real numbers is the union of the set of rational and Irrational Numbers. But there are so many other ways to describe it. Real numbers can be constructed as Dedekind cuts of rational numbers. The set of real numbers can also be viewed as the set of equivalence classes of Cauchy sequences of rational numbers Some people like the definition, that the real numbers are all the numbers which can be expressed as decimals.
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In a certain sense, the set of complex numbers is "larger" than the set of real numbers, since the set of real numbers is a proper subset of it.
Real numbers are a proper subset of Complex numbers.
Are disjoint and complementary subsets of the set of real numbers.
There is only one set of Real numbers.
By definition, it is the set of all real numbers!