Weierstrass functions. Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere".
Here is an example of one: It is not hard to show that this series converges for all x. In fact, it is absolutely convergent. It is also an example of a fourier series, a very important and fun type of series. It can be shown that the function is continuous everywhere, yet is differentiable at no values of x. Imaging maths - Inside the Klein bottle. I Hate Math! (Not After This, You Won't) : Krulwich Wonders… A musician wakes from a terrible nightmare.
In his dream he finds himself in a society where music education has been made mandatory. "We are helping our students become more competitive in an increasingly sound-filled world. " Educators, school systems, and the state are put in charge of this vital project.