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Problem with Sets

  1. Sep 26, 2010 #1
    Hi, I'm having a lot of trouble with the following question:

    1. The problem statement, all variables and given/known data

    (a) Let x,y ∈ Z. Prove that if x>0 and x+y <xy, then y>0

    2. Relevant equations
    x+y <xy, then y>0

    3. The attempt at a solution

    I am very confused with this problem, and am not even sure on how to start. Any tips/suggestions to help me get started would be greatly appreciated.
  2. jcsd
  3. Sep 26, 2010 #2
    What properties does Z have ? Is it an ordered feild ? A commutative ring , a subset of R etc. Without this information I do not see how we can help you.
  4. Sep 26, 2010 #3


    Staff: Mentor

    Z is just the set of integers.
  5. Sep 26, 2010 #4


    Staff: Mentor

    I think this might be a way to prove it, using a proof by contradiction.

    Assume that x and y are in Z, x + y < xy, and y <= 0.

    Since by assumption, y <= 0, then x + y <= x.
    Then (x + y)2 <= x2
    From the above, it follows that y(2x + y) <= 0.

    Now, work with that inequality to try to get a contradiction, keeping in mind that x and y can only be integer values, and that x > 0 and y <= 0.
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