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 December 30th, 2016, 12:57 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} 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 07:07 PM.
 December 30th, 2016, 07:19 PM #2 Global Moderator   Joined: Dec 2006 Posts: 17,734 Thanks: 1360 Should "finish" be "finite"?

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