# Riemann's Example of a Continuous but Nowhere Differentiable Function

Riemann's Example of a Continuous but Nowhere Differentiable Function

Contrary to intuition, functions exist that are continuous everywhere, but differentiable almost nowhere. This shows a plot of partial sums of Riemann's continuous but nowhere differentiable function which can be expressed as .

∞

∑

k=1

αcos(πx)+(1-α)sin(πx)

β

k

β

k

β

k