Darboux function
From specialfunctionswiki
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.
Properties
Theorem: The Darboux function is continuous.
Proof: █
Theorem: The Darboux function is nowhere differentiable.
Proof: █
