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

  • Thread starter rad0786
  • Start date
188
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1. Homework Statement

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. Homework 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?
 

Answers and Replies

188
0
Never mind people, after a lot of hard thinking, i got it (well...close to it!)
 

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