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What is set of irrational numbers union with rational numbers?
The real numbers.
Why does any real number must be either a rational number or an irrational number?
It is due to the fact that the set of real numbers is defined as the union of the rational and irrational numbers.
What rational numbers are real numbers?
All rational numbers are real numbers.
What is the relationship between real number and rational number?
Rational numbers form a proper subset of real numbers. So all rational numbers are real numbers but all real numbers are not rational.
Set of real numbers?
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.
