Van der Waerden function
From specialfunctionswiki
The van der Waerden function is defined by the formula $$V(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{1}{10^k} \underset{m\in\mathbb{Z}}{\inf} |10^k x-m|.$$
Properties
Theorem: The van der Waerden function is continuous.
Proof: █
Theorem: The van der Waerden function is nowhere differentiable on $\mathbb{R}$.
Proof: █
