The following example was brought up in two different classes that I am taking, within a couple days of each other. It is the classic example of an immeasurable set on the interval [0,1]. Now in math, words like measure and measurable have technical definitions, and lead to bizarre results like the Banach-Tarski paradox. I’m going to give a fairly informal explanation here. Continue reading

# Category Archives: Analysis

# #5: The Cantor Set and the Cantor Function

The **Cantor set** is a fractal that is obtained by repeatedly removing the middle third of a segment. Start with the closed interval . Remove the open interval to obtain , i.e. two disjoint closed segments. Remove the middle thirds of those two segments, and you end up with four disjoint segments. After infinitely many steps, the result is called the **Cantor set**. The diagram below is only an approximation after a finite number of steps.