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
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That term, over there!
No, it is imaginary. Irrational numbers are a subset of real numbers Real numbers and imaginary numbers are sets without any overlap.
You have it backwards. Integers are a subset of real numbers.
The real numbers, themselves. Every set is a subset of itself.
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.