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
re: Not dense enough ... by vswitchs)
Thanks for your comment and support, vswitchs.
The function that you reference, at
http://www.math.tamu.edu/~tom.vogel/gallery/node7.html, is very
interesting, and it is in fact very similar to mine. For that
function, (f(x)-f(y))/(x-y) is always between -1 and 1. So you
can make that function monotonic by just adding g(x) = 3x, after which
(f(x)-f(y))/(x-y) is always between 2 and 4. If it is in fact
differentiable nowhere (which I am not sure of yet), then it is a
solution to this problem after adding g(x).
re(2): Not dense enough ...
