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It is the set of Real numbers.
The intersection between rational and irrational numbers is the empty set (Ø) since no rational number (x∈ℚ) is also an irrational number (x∉ℚ)
The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.
A set which contains any irrational or complex numbers.
The real number system