1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof: (Pigeon Hole Principle) from a Problem Solving Class

  1. Jan 13, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that THEIR EXISTS INTEGERS a,b,c NOT ALL 0 AND EACH OF ABSOLUTE VALUE <10^6 SUCH THAT
    |a + sqrt(2)*b + cuberoot(3)*c| < 10^-11


    2. Relevant equations


    |a + sqrt(2)*b + cuberoot(3)*c| < 10^-11


    3. The attempt at a solution

    Well, I know that we have to use the pigeon hole principle, otherwise I am completely lost.

    I did try to actually find values for a,b,c ... but no luck with that.

    I am now attempting to rearrange the formula and solve for some variable in terms of another.

    Has anybody seen a problem like this before? Does it have a name?
     
  2. jcsd
  3. Jan 13, 2007 #2
    Never mind people, after a lot of hard thinking, i got it (well...close to it!)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?