In a similar vein, the cantor function [1] (also known as the devil's staircase) is continuous and has derivative 0 almost everywhere, but still manages to incr

In a similar vein, the cantor function [1] (also known as the devil's staircase) is continuous and has derivative 0 almost everywhere, but still manages to increase in value. [1] http://en.wikipedia.org/wiki/Cantor_function#Properties http://en.wikipedia.org/wiki/Cantor_function#Properties