Originally Posted by

**thyristor**
Hi!

Sorry for my late reply; I have been quite busy the last days and forgot about our ongoing discussion. I thank you for the document you provided, but actually I don't think your conclusion is quite correct. To demonstrate this, take for example the Weirstrass function. Just like my function, it is continous and defined at all points on some interval, so (1) and (3) from your last posts cannot hold. So in order for the Wierstrass function not to be differentiable, every point on some interval has to be a corner point. Following your own argument, we conclude that this implies the existence of RHD and LHD, violating the definition of the Weierstrass function and thus, incorrectly, proving it cannot exist.

The problem here is that corner-point either has to be redifined, or the statement in the provided document has to be redfined.