All rational numbers are real so the phrase "real rational" has no meaning.
There are an infinite number of subsets:
The emply or null set,
{1,1.5, 7/3},
{2},
(0.1,0.2,0.3,0.66..., 5.142857142857...} are some examples.
Rational numbers.
Both are subsets of the real numbers.
The two main DISJOINT subsets of the Real numbers are the rational numbers and the irrational numbers.
Both rational numbers and integers are subsets of the set of real numbers.
Rational Numbers and Irrational Numbers
rational numbers and irrational numbers
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
There are no subsets of irrational numbers. There are subsets of rational numbers, however.
Integers, Rational numbers, Real numbers and Complex numbers.
Are disjoint and complementary subsets of the set of real numbers.
The rational numbers are a subset of the real numbers. You might recall that rational numbers are those that can be expressed as the ratio of two whole numbers (no matter how large they are). Irrational numbers, like pi, cannot. But both sets (the rational and irrational numbers) are subsets of the real numbers. In fact, when we look at all the numbers, we are looking at the complex number system. We break that down into the real and the imaginary numbers. And the real numbers have the rational and irrational numbers as subsets. It's just that simple.
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.