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Construction of the Real Numbers

  1. Dec 25, 2009 #1


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    Does anyone have or know of any good books that cover the construction of the real numbers via cauchy sequences? I would appreciate any recommendations. Thanks!
  2. jcsd
  3. Dec 25, 2009 #2
  4. Dec 25, 2009 #3
    rudin doesn't use cauchy sequences - it uses dedekind cuts.
  5. Dec 25, 2009 #4
    Hmm, I think Spivak includes this construction as an exercise. IIRC, he guides you along so you get the basic idea, but the tricky parts such as demonstrating the existence of a multiplicative inverse is left entirely to you. If you want to just read about it, Terence Tao's lecture notes might be helpful:

  6. Dec 25, 2009 #5
    Last edited by a moderator: Apr 24, 2017
  7. Dec 28, 2009 #6


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    Axiomatic Set Theory by Suppes. You can browse through it with Google Books, see page 188.
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