Difference between revisions of "Faber F1"
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Revision as of 18:34, 24 May 2016
The Faber function $F_1$ is defined by $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|.$$
Plot of $F_1$.
Properties
Theorem: The Faber function $F_1$ is continuous.
Proof: █
Theorem: The Faber function $F_1$ is nowhere differentiable.
Proof: █
