Does anyone know how to do this problem, because i have no idea on this one
All I have so far is the base case. If you set n = 1 then you have a set with 2 (or n+1 = 1+1) positive integers where both integers have to be less than or equal to 2 (or 2*n = 2*1) so the only option is that the set contains the numbers 1 and 2. For this set it is true that at least one integer in the set divides another integer in the set since 2 is divisible by 1. Does this sound right to anyone else? I'm not sure how to complete the inductive step.
-Rachel
I believe that is correct for the base case. I am also stuck on the inductive step. If we assume that k is true, then k+1 integers, each less than 2k, must have k or fewer prime numbers. I'm stuck on the next part. How do I prove that k+2 integers, each less than 2k+2, have fewer than k+1 prime numbers?
--Jberlako 19:47, 21 January 2009 (UTC)
