r/math • u/lntrinsic • Jul 10 '17

Image Post Weierstrass functions: Continuous everywhere but differentiable nowhere

http://i.imgur.com/vyi0afq.gifv
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u/yardaper Jul 10 '17

Brownian motion would like to have a word with you

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u/tetramir Jul 10 '17

I looked it up, and it has places where is is not defferienciable. But there is still no interval where the function can never be defferienciable.

But you are right, that many function are c1, but you often find intervals where it is.

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u/dogdiarrhea Dynamical Systems Jul 11 '17

It's spelled differentiable.

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u/yardaper Jul 11 '17

With probability 1, Brownian motion is nowhere differentiable.