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Construction of the Real Numbers

  1. Dec 25, 2009 #1

    jgens

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    Gold Member

    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:

    http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/week2.pdf
     
  6. Dec 25, 2009 #5
    Last edited by a moderator: Apr 24, 2017
  7. Dec 28, 2009 #6

    Landau

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    Science Advisor

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