In class today, we discussed the Cantor Set, one of the earliest examples of a mathematically defined fractal. It has three important properties:
- It has a total length of zero
- Every point in the set is a limit point
- 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.