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.

Nice to see someone is still having a bit of fun with this. Not sure if adding up piecewise linear functions work, at least this is not the approach I used. Take a look at the Cantor function, it gets you a looong way because it already has lots of non-differentiability points.

Posted by JLo on 2006-10-31 06:55:10