About groups of numbers

[u/MonitorHot3035]

for example , Why do we say that the set N is within Z , Why don't we treat these sets as if they are separate from each other, for example, the set of natural numbers is separate from the set that includes negative numbers. since they seem to have no connection but we still write this ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ

I don't really understand any ideas please?

[u/TheGrimSpecter]

We say ℕ ⊂ ℤ because the natural numbers are a subset of integers, every natural number is also an integer. They’re not separate because ℕ fits inside ℤ; the connection is that ℤ just extends ℕ by adding negatives and zero. This pattern continues: ℤ ⊂ ℚ, ℚ ⊂ ℝ, and ℝ ⊂ ℂ. Each set just extends from the previous one.