My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum

LinkBack Thread Tools Display Modes
December 30th, 2016, 12:57 PM   #1
Joined: Dec 2016
From: France

Posts: 1
Thanks: 0

dense set

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 07:07 PM.
iraqdil is offline  
December 30th, 2016, 07:19 PM   #2
Global Moderator
Joined: Dec 2006

Posts: 18,956
Thanks: 1603

Should "finish" be "finite"?
skipjack is offline  

  My Math Forum > College Math Forum > Topology

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 07:38 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 01:44 PM
Showing something is dense in .... babyRudin Real Analysis 8 September 24th, 2008 07:30 AM

Copyright © 2018 My Math Forum. All rights reserved.