Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
I found this question here, the question seems much interesting but for obvious reason it is closed there, I was wondering how to derive such a function?
2026-04-07 06:29:17.1775543357
Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
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You could take $$f(x)=\begin{cases}1&x\in \mathbb Q \\ -1&x\in\mathbb R\setminus\mathbb Q\end{cases}$$