(March 22, 2018 at 9:58 pm)Grandizer Wrote: I sort of see it now. It seems it's all about continuing the pattern to infinity, starting from an intuitive sawtooth function.
The basic idea is to make sure the problem points get distributed throughout the interval while keeping the function continuous.
In the sin(3^n x)/2^n , the ide is that we have functions of smaller and smaller amplitude but larger and larger derivatives added up in a way that 'problems mount up' at any point.
There is a much deeper result is that *any* continuous function can be approximated as well as you like by a continuous nowhere differentiable function.
