Foundations Construction of the Number Systems ... Natural, Integers, etc

[Math Amateur]

At present I am trying to understand the construction of the number systems ... natural, integers, rationals and reals ...

What do members of PFs think is the clearest, most detailed, most rigorous and best treatment of number systems in a textbook or in online notes ... ?

NOTE: I am currently using Ethan D Bloch: "The Real Numbers and Real Analysis" ... ... where the coverage is detailed ... and proofs in particular are detailed and in full ... but some of the explanations are not particularly clear ... ...Peter

 

[jambaugh]

I think most any analysis text will be sufficiently clear and rigorous. The only odd step is the filling out of the real numbers as Dedekind cuts on the set of all rational numbers.

Now an interesting approach which extends much further is Conway's "On Numbers and Games".

 

[Math Amateur]

Thanks Jambaugh ... appreciate your help ...

Peter