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Dedekind cut

  1. Sep 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that for any two Dedekind cuts A,B, there exists a unique cut C such that A+C=B

    2. The attempt at a solution

    In order to prove this, I need to prove the existence and uniqueness of such a cut.

    For the existence, I started by considering a cut for which this works: C={b-a, b \in B, a \in \mathbb{Q}-A} but I am having trouble showing it is a cut.

    For the uniqueness, I want to consider two cuts C and C' such that C≠C' and I wanted to show that C is not a subset of C' and C' is not a subset of C. However, could someone help me to prove this ?

    Thank you in advance
     
  2. jcsd
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