# What's a good source on how to construct all sets of numbers?

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.

• You could also have a look at John Conway's On Numbers And Games. – Gerry Myerson Nov 16 '17 at 6:05
• What's $\Bbb P$? – user228113 Nov 16 '17 at 6:28
• You acn see Jürg Kramer & Anna-Maria von Pippich, From Natural Numbers to Quaternions, Springer (2018). – Mauro ALLEGRANZA Nov 16 '17 at 7:19
• @G.S, from context, I'd say the real algebraics. – Gerry Myerson Nov 16 '17 at 12:10
• In my answer to Is the real number structure unique?, I posted a list of 9 textbooks each of whose primary purpose is the construction of various number systems. – Dave L. Renfro Nov 16 '17 at 13:02