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 work everyone! I think I owe you a hint or two:

A solution can be constructed in a similar manner as in the first function challenge (my solution, not Ken's), but instead of starting with a simple step function, you'll need a more complex ingredient. It showed up in some comments or solution of the first challenge.

Don't try to construct a function that is monotonic and non-differentiable everywhere, because it can be shown that the non-differentiability points of a monotonic function are a very thin set.

Posted by JLo on 2006-10-15 11:08:58