Faber F1

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The Faber function $F_1$ is defined by $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|.$$

Properties

Theorem: The Faber function $F_1$ is continuous.

Proof:

Theorem: The Faber function $F_1$ is nowhere differentiable.

Proof:


See Also

Faber function F2

References

[1]