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Infimum homework problem

  • Thread starter muso07
  • Start date
  • #1
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Homework Statement


Find inf{|x-pi|:x[tex]\in[/tex]Q}

Homework Equations



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. :)
 

Answers and Replies

  • #2
HallsofIvy
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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.
 
  • #3
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Thanks for the clarification. :)
 

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