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Density of a specific set

  1. Oct 11, 2010 #1
    Is there an easy way to prove that for any irrational [tex]\xi[/tex] the set:

    [tex]\{x \in \mathbb{R}: x = p + q\xi, \ p, q \in \mathbb{Z}\}[/tex] is dense in [tex]\mathbb{R}[/tex]?

    I know a proof involving notions from measure theory of which I unfortunately know nothing about. Any help would be very appreciated.
    Last edited: Oct 11, 2010
  2. jcsd
  3. Oct 11, 2010 #2
    Nevermind, it turned out to be rather easy.
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