I'm trying to remember a function used in my college calculus text as an example of a degenerate case. The function was continuous at every point in (-inf, inf), but not differentiable at any point. Any of you math heads know what function I'm talking about?
Yeah, I remember this one. Start with a sawtooth wave. Halve its amplitude and double its frequency. Repeat this process indefinitely. Sum all the functions. The resulting function is continuous everywhere, but nowhere differentiable.
The limit of the Koch curve should have that property, but I do not know of an an expression for it it. I do not remember any such function with an expression describing it.
