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Fat Cantor Set question

  1. Aug 20, 2007 #1
    Let C be the thick Cantor set. let {a_n} be a sequence of positive numbers.
    In the construction of the thick Cantor set, at the n-th stage we remove the middle a_n part of each interval (instead of the middle third as in the ordinary Cantor set).

    I actually wanted to show that [0,1]-C is dense (where C is the thick Cantor set). How do I show it?
  2. jcsd
  3. Aug 20, 2007 #2


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  4. Aug 20, 2007 #3
    I would prove the following. Let [itex]x\in C[/itex] be arbitrary. It suffices to find a sequence [itex]x_n\in [0,1]-C[/itex] so that [itex]x_n\to x[/itex]. Do you know how to identify points of Cantor's set with sequences of 0 and 1? I mean sequences like 0011... 1010... 1101... and so on.
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