Fractals & Chaos Assignment for 9/11

In class today, we discussed the Cantor Set, one of the earliest examples of a mathematically defined fractal. It has three important properties:

  1. It has a total length of zero
  2. Every point in the set is a limit point
  3. The set has uncountably infinite number of points

As we discussed in class, the set of real numbers between [0,1] has properties 2 and 3, but has a length of 1. The set of rational numbers between [0,1] has properties 1 and 2, but not 3. Your homework is to think of a set of numbers that has properties 1 and 3, but not 2. As a hint, consider a modification of the Cantor Set.

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