Challenge

Write down the numbers 1,2,...,2n for some positive integer n. Now out of these choose n+1 numbers. Prove that out of these n+1 numbers there exists numbers a and b such that a divides b.

demonstration/example.
1,2,3,4  n=2 so n+1=3.
The only set that doesn't contain 1 is {2,3,4} and 2|4.

I think I can finish >>4's argument.  Let the chosen numbers consist of p evens and n+1-p odds.
Case 1: One even number divides another, easy.
Case 2: No even number divides another.  Thus, there are p even numbers whose odd prime factorizations are different.  n+1-p odd numbers were chosen.  [1,2n] contains n odd numbers.  Since (n+1-p)+p = n+1 > n, the sets {odd factors of chosen even #s} and {chosen odd #s} must overlap, and one of the odds has to divide one of the evens.  Amirite?