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I read the construction of real numbers by Dedekind cuts today in a book(it was quite incomplete).I was wondering if someone could please point me to a source or a book containing the construction of the entire natural numbers,the rationals, the real numbers and the various operations like addition, subtraction, exponentiation and all that. I may not read it whole at one go but I certainly wish to see how it is done.In addition, a few "exercises" or something of that sort will not do me harm.

Thanks!

Squid
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    I start from the natural numbers in this post. I'm sure you can find detailed constructions of the natural numbers on the internet somewhere too. – Zhen Lin Sep 12 '12 at 17:43
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    for dedekind, http://books.google.com/books?id=PywPAAAAIAAJ&printsec=frontcover&dq=dedekind+real+numbers&source=bl&ots=M79IBx6ofg&sig=Pb1jsc2Xraq5XVJNvqnWy0gjSko&hl=en&sa=X&ei=2w1RUJC-MunFyAHi4IHYDQ&ved=0CC0Q6AEwAA#v=onepage&q=dedekind%20real%20numbers&f=false – yoyo Sep 12 '12 at 22:34

2 Answers2

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Goldrei's "Classic Set Theory" is a great introduction! The first few chapters are dedicated to this.

  • I don't know why these answers have not yet received upvotes.But this is precisely what I was looking for.Thanks for sure. – Squid Sep 12 '12 at 19:41
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Here you will find a book that contains the construction. It is an appendix to chapter 1.

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