Weierstrass Function
The graph of the n-th partial sum for Weierstrass's monster. To get a better idea about the limit, try larger values of n (values larger than 30 do not work due to roundoff errors). Try to zoom into the function using the mouse. Can you believe that this function is continuous, but differentiable nowhere ? |
Proof:
This function, incidentally, is the one which was used to generate the logo at the title pages. To show that it is continuous, check the entry in the chapter on function sequences and series. To show it is not differentiable will be somewhat more difficult.We'll do it later ...