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Infimum homework problem

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Find inf{|x-pi|:x[tex]\in[/tex]Q}

    2. Relevant equations

    3. The attempt at a solution
    I was thinking that the greatest lower bound must be 0, but that seemed a bit simple. Is there any justification I have to give for this?

    Any help would be much appreciated. Cheers. :)
     
  2. jcsd
  3. Mar 4, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Infimum

    Yes, there exist rational number arbitrarily close to any real number and, in particular, arbitrarily close to [itex]\pi[/itex]. The infimum of [itex]|x- \pi|[/itex] for x rational is 0.
     
  4. Mar 4, 2010 #3
    Re: Infimum

    Thanks for the clarification. :)
     
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