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Analysis - How many numbers in the interval [0,1) contain 5 consecutive 5's?

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data

    Let E be the set of points in [0,1) whose decimal expansion contains somewhere the block 55555. Find the measure of E.


    2. Relevant equations



    3. The attempt at a solution

    I have a feeling that in order to find the measure of E, I should find the measure of the complement of E and then subtract it from 1. The complement of E would be the points in [0,1) containing no 5's, containing no consecutive 5's, containing 2 consecutive 5's, containing 3 consecutive 5's, containing 3 consecutive 5's, or containing 4 consecutive 5's. I'm not sure how to compute the measure of this set, however.

    Any help would be greatly appreciated!
     
  2. jcsd
  3. Sep 25, 2011 #2

    Dick

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    Homework Helper

    Well, start your program. What the measure of all of the points that contain no 5's at all? This is rather like a Cantor set.
     
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