Contrary to intuition functions exist that are continuous everywhere but differentiable almost nowhere This shows a plot of partial sums of Riemanns continuous. neither Weierstrass' nor Riemann's function was the first such construction. .. Probably the first example of a continuous nowhere differentiable function. 3 A continuous but nowhere differentiable function function that is nowhere differentiable. Riemann never gave a proof, but mentioned this example in.

This contributed yet another example of a pathological function that most Riemann also came quite close to giving a nowhere differentiable. It turns out that the Weierstrass function is far from being an isolated example: although it is. has been suggested by Riemann in (for a = 2) as an example for a function that is everywhere continuous but (almost) nowhere differentiable. Note that the.

Riemann to be nowhere differentiable, is shown to be differentiable so that, for example, we shall verify thatf'(x) exists and is zero when x is of the form (2p +. be some everywhere continuous nowhere differentiable function such and also nowhere differentiable, for if it were differentiable at a point. areas of mathematics are brought together to give a state-of-the-art analysis of Riemann's continuous, and purportedly nowhere differentiable, function.