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Can I generate a continuous and non-differentiable function with basic calculus tools? Is there a simple way of expressing such a function?

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Non-differentiable everywhere? At a point? What do you mean by "basic calculus tools"? –  Pedro Tamaroff Aug 19 '13 at 1:42
    
It was supposed to be a function ND at infinite if not at all points in x-y plane.Soryy<I coud'nt put my point clearly. –  RamChandra Aug 19 '13 at 2:04
    
I spelt sorry wrongly.By the waycan you tell me what's the difference between a class and a set? –  RamChandra Aug 19 '13 at 2:07

1 Answer 1

The function $|x|$ is (uniformly) continuous everywhere, but not differentiable at $0$, because it has a corner. Finite sums of this function can give continuous maps which are not differentiable at any given finite set, and careful scaling can extend this to countable sets.

A continuous function which is nowhere differentiable is harder to construct, but quite doable with infinite series.

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That was helpful.I realize that I was dumb enough to miss that point. –  RamChandra Aug 19 '13 at 2:03
    
If $\psi(x) = 1_{[-1,1]}(x)(1-|x|) $, and we let $f(x)=\sum_n \psi(x-n)$, then $f$ is not differentiable on $\mathbb{Z}$. –  copper.hat Aug 19 '13 at 3:04
    
Yeah! something that uses the same concept on ND of modulus at a point –  RamChandra Aug 19 '13 at 11:42

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