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Proof in set theory.

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    {1/x+1/y / (x,y) in (IN*)^2} subset of ]0,2]

    2. Relevant equations



    3. The attempt at a solution

    When x=y=1 u get a sum of 2 which is in ]0,2] and for any x and y greater than 1 u get a sum between 0<sum≤2.
    It's a simple problem but i just don't know how to show the proof. Some help please.
     
  2. jcsd
  3. Oct 18, 2011 #2

    Mark44

    Staff: Mentor

    What is this supposed to mean?
     
  4. Oct 18, 2011 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Do you mean to say that

    [tex]\{1/x+1/y~\vert~x,y\in \mathbb{N}\setminus\{0\}\}[/tex]

    That would make sense...

    So you need to show that

    [tex]\frac{1}{x}+\frac{1}{y}\leq 2[/tex]

    for all naturals x and y. Maybe use the fact that

    [tex]\frac{1}{x+1}\leq \frac{1}{x}[/tex]

    and do induction??
     
  5. Oct 19, 2011 #4
    Yep that's exactly what I wanted to say. thank you.
     
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