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Thread: Set Theory(Try #2) and analysis

  1. #1
    Dec 2006

    Set Theory(Try #2) and analysis

    I apologize for the unclear post earlier. However, that is exactly how the question reads in the book. Let me see if I can clarify.

    r + s = {p + q: p in r and q in s}

    I need to show that r + s is a real number. I am assuming that I show this by using a Dedekind left set and proving that:

    1) r is proper, non-empty subset
    2) r is close to the left
    3) r has no maximum element

    I need to show the same for r x s.

    My trouble with this, is that I am inexperienced at writing proofs and often need help with the "acceptable" notion. I am continuing to learn what statements actually prove what I am trying to prove and it is helpful to see another person's thought process. Unfortunately, I go to a university that refuses to teach me "how" to write a proof.

    Thanks for the help.
    Last edited by taypez; Feb 5th 2007 at 03:58 PM. Reason: adding info
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  2. #2
    MHF Contributor

    Aug 2006
    Ah! You are using Dedekind Cuts to define a real number.
    Walter Rudin’s book, Principles of Mathematical Analysis, is perhaps the best reference on the construction of the reals using Dedekind Cuts. You can find that text in any mathematics library. You need to understand how addition and multiplication are defined using Dedekind Cuts.
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