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Function example? Continuous everywhere, differentiable nowhere

Is there any function that continuous in all places and not differentiable in all places?

do you know a good book about this?

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marked as duplicate by Hagen von Eitzen, Micah, Martin Argerami, Henry T. Horton, Hans Lundmark Dec 1 '12 at 19:12

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

I added the reference-request tag as you ask for a book. – Hagen von Eitzen Dec 1 '12 at 17:59
Nice additional information: A randomly chosen continuous function is nearly "always" not differentiable in all places. For example the continous functions on $\left[0,1\right]$ that are not differentiable in all places are dense in all continous function on $\left[0,1\right]$ – user127.0.0.1 Dec 1 '12 at 18:15
up vote 1 down vote accepted

You could take a look at the Weierstrass function. There you can also find a list of references. "Counterexamples in analysis" of Gelbaum and Olmstead sounds very promising.

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