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No. Fractions do not include Irrational Numbers. And although there are an infinite number of both rationals and irrationals, there are far more irrational numbers than rationals.
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Is the densest subset of real numbers is set of fractions?
No, the irrationals are more dense.
Is real numbers a subset of Integers?
You have it backwards. Integers are a subset of real numbers.
Which is the largest subset of a real numbers?
The real numbers, themselves. Every set is a subset of itself.
What are the hierarchy of real numbers?
Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.
Which sets of numbers are a subset of the real numbers?
The natural numbers (ℕ) are a subset of the integers (ℤ) which are a subset of the rational numbers (ℚ) which are a subset of the real numbers (ℝ): ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ → ℕ ⊂ ℝ and ℤ ⊂ ℝ as well as ℚ ⊂ ℝ
