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Homework Help: Cantor set and Base 3 expansion

  1. Sep 23, 2006 #1
    How do I do a ternary expansion of numbers, and prove that if a number is part of the 2^k iteration of the cantor set if and only if each decimal expansion position is either a two or zero? If you guys can give me a hint, I would love to go from there.
  2. jcsd
  3. Sep 23, 2006 #2


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    I think you have that wrong. A number is in the set formed after the kth iteration of the process of removing middle thirds used to create the cantor set iff the kth digit in its base 3 expansion is not 1 (more specifically (to handle endpoints like 1/3=0.1=0.0222...), if it can be written in such a form). Since this is true, maybe it will be easier to prove.
  4. Sep 23, 2006 #3

    You are right. Thanks a lot. I didnt realize this resource was availabe and hopefully will be able to contribute both ways.
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