Difference between revisions of "Darboux function"
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Revision as of 18:34, 24 May 2016
The Darboux function is defined by $$D(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\sin\left((k+1)!x\right)}{k!},$$ where $\sin$ denotes the sine function.
Plot of $D(x)$ on $[0,5]$.
Properties
Theorem: The Darboux function is continuous on $\mathbb{R}$.
Proof: █
Theorem: The Darboux function is nowhere differentiable on $\mathbb{R}$.
Proof: █
