Find a continuous, strictly monotonic function f:R->R (R the set of real numbers) which is non-differentiable on a very dense set.

For this problem, we'll call a set of real numbers very dense if it intersects every interval [a,b] in an infinite, uncountable number of elements.

I'm not ignoring this problem.  I have a germ of an idea, involving a base two representation, but it still needs some work.

Posted by Steve Herman on 2006-10-02 21:10:55