The Real numbers
All rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions.
No, a number is either rational or irrational
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.
the set of real numbers
It is the set of Real numbers.
All irrational numbers, complex number and so on.