1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

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

Have something to add?

Similar Discussions: Cantor set and Base 3 expansion
  1. Cantor Sets (Replies: 5)

  2. Cantor Set (Replies: 2)