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.

(In reply to I'm still here ... by Steve Herman)

Hi Steve, good to know you're still there! I am also having doubts whether piecewise linear functions work as building blocks to the function I am after. But who knows, last time round Ken surprised us with an unexpected solution, this may happen again. Strictly speaking of course, the infinite sum may very well have more non-diff points, e.g. the Weiserstrass-Function is a summation of very smooth functions (differentiable everywhere) but the sum is differentiable nowhere.

Posted by JLo on 2006-10-31 10:04:48