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.
Nothing new to contribute. I agree with vswitchs' point that any
summation of countable functions which have a countable number of
non-differentiable points results in a final function which has a
countable number of non-differentiable points.
I'm still here ...
