The real numbers.
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It is due to the fact that the set of real numbers is defined as the union of the rational and irrational numbers.
real numbers
The set of real numbers.
The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.
The set of Real numbers.