Difference between revisions of "Van der Waerden function"
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| + | =See Also= | ||
| + | [[Takagi function]] | ||
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[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] <br /> | [https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] <br /> | ||
Revision as of 23:07, 31 December 2015
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: █
