Takagi function

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The Takagi function (also called the blancmange function) is defined by $$\mathrm{takagi}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{\mathrm{dist}_{\mathbb{Z}}(2^n x)}{2^n}.$$

Properties

Theorem: The Takagi function is continuous on $\mathbb{R}$.

Proof:

Theorem: The Takagi function is nowhere differentiable on $\mathbb{R}$.

Proof:

See Also

van der Waerden function

References

[1]
[2]