1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted