Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Possible Duplicate:
Are Continuous Functions Always Differentiable?

Is there a continous function (continous in every one of its points) which is not differentiable in any of its points?

share|improve this question

marked as duplicate by Isaac Solomon, Américo Tavares, froggie, no identity, Nate Eldredge Nov 22 '12 at 18:17

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.

4  
Yes. The standard example is the Weierstrass function. –  froggie Nov 22 '12 at 17:42
1  
Or a Wiener process - note the "fractal" nature of the image. –  kahen Nov 22 '12 at 17:44
1  
Yes, most (in the sense of category) continuous functions are nowhere differentiable. –  André Nicolas Nov 22 '12 at 17:49
1  
this might help –  no identity Nov 22 '12 at 17:56
1  
@Andris: Look at the continuous functions from $[0,1]$ to the reals, under the sup norm. Then the set of such functions that are continuous somewhere is meager. Standard result, I think it is in Oxtoby, but it should not be hard to track down a proof on the Web. –  André Nicolas Nov 22 '12 at 18:10

1 Answer 1

up vote 1 down vote accepted

Yes, for example the Weierstraß function.

One can actually show that the set $A:= \{f \in C[0,1]; f$ has no right-derivative in any point in $[0,1)\}$ is dense in $C[0,1]$ and uncountable.

share|improve this answer
    
You can do even better: $A$ is co-meagre in $C[0,1]$. –  kahen Nov 22 '12 at 18:04

Not the answer you're looking for? Browse other questions tagged or ask your own question.