December 30th, 2016, 01:57 PM  #1 
Newbie Joined: Dec 2016 From: France Posts: 1 Thanks: 0  dense set
Hello, I'm here to ask you your help. I have to do an exercise, but I have difficulties to finish. Let a and b be two reals strictly positive such that a/b is irrational. First, I have demonstrated that G=aZ+bZ is dense and then I have demonstrated that if A is a dense set and F a finish set, then A\F is also a dense set. This is now that I freeze. Let N be a natural number. With the help of the last question, demonstrate that for all r>0, there exist two relatives number p and q such that: p>=N and ap+bq<= r We can use the set F={ap+pq, such that p<N and q<M} for a good choice of M. Deduce that the set {ap+bq, and p>=N} is dense in R. My research: I found M=(r+aN)/b And then I found that the F set is a finish set. But I don't know how to go further. Thanks for your help. Last edited by skipjack; December 30th, 2016 at 08:07 PM. 
December 30th, 2016, 08:19 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 16,590 Thanks: 1199 
Should "finish" be "finite"?


Tags 
dense, set 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Dense sets  limes5  Real Analysis  6  June 21st, 2013 01:02 PM 
proof the set Q\N is dense in R  himybrother  Applied Math  3  November 6th, 2011 08:38 PM 
Q is dense in R  guynamedluis  Real Analysis  3  March 29th, 2011 05:42 PM 
Dense set  problem  Cogline  Real Analysis  1  January 31st, 2010 02:44 PM 
Showing something is dense in ....  babyRudin  Real Analysis  8  September 24th, 2008 07:30 AM 