This is one I am having a lot of difficulty with. I'm not sure how to show that the Cantor function (or 'Devil's Staircase) is not Lipschitz.
Hint: For every nonnegative integer $n$, find some points $x_n$ and $y_n$ such that $|x_n-y_n|=1/3^n$ and $|f(x_n)-f(y_n)|=1/2^n$. Conclude.
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