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Proving aspects of a set

  1. Oct 17, 2010 #1

    silvermane

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    Gold Member

    1. The problem statement, all variables and given/known data
    We have U = { 3n/(n+1) : n in N }

    i. Prove that U is non-empty and bounded above by 3.
    ii. Prove that if a is a real number with a<3, then there is an n in N such that a < 3n/(n+1)


    3. The attempt at a solution

    i. We can show it non-empty by saying that 3/2 is in the set since 3*1/(1+1) = 3/2, but I'm a little confused in how to prove that 3 is an upper bound, and that a is smaller than our equation. :(

    I don't want answers, but hints and tips are greatly appreciated :))))
     
  2. jcsd
  3. Oct 17, 2010 #2
    n/(n+1) < 1
     
  4. Oct 18, 2010 #3

    HallsofIvy

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    Science Advisor

    Well, if you want to do it the easy way!

    I was all set to do a proof by induction on n!

    To get the last, that if a< 3 then there exist an integer n such that a< n/(n+1), try solving for n.
     
  5. Oct 18, 2010 #4
    XD.

    Are you sure you don't want to use some complex analysis ? :p
     
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