Lately I've been interested in building, formally, all sets of numbers, starting from ℕ, then ℤ, then ℚ, then ℙ, then ℝ, then iℝ, then ℂ.
The only book I have come up, so far, is "Foundations of analysis" by Edmund Landau, which seems to build them like this : ℕ, ℤ and ℚ, ℝ, ℂ. Is that one a good book? which other source would you recommend?
This would also include the mathematical operations each set has.
Also, I'm corious about why ℕ⊂ℤ⊂ℚ, (ℚ∪ℙ)⊂ℝ, ..., and so on.
Thanks in advance.