Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

  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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?