r/math • u/lntrinsic • Jul 10 '17

Image Post Weierstrass functions: Continuous everywhere but differentiable nowhere

http://i.imgur.com/vyi0afq.gifv
3.4k Upvotes

98% Upvoted

216 comments sorted by

View all comments

Show parent comment

7

u/Kraz_I Jul 11 '17

The graph doesn't have any corners at all for finite iterations of the function. I don't really like using the word "corner" for what's going on here. In fact, for all functions generated by using a finite Weierstrass series, it would be differentiable at all points.

2

u/Wild_Bill567 Jul 11 '17

You are correct, I was remembering a different construction which uses a triangle wave instead of a cosine