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# Continuity problem #2

Find an example of a function that is nowhere continuous but whose absolute value is everywhere continuous.

Note by Hobart Pao
1 year, 9 months ago

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$f : \mathbb{R} \to \mathbb{R}, \forall x f(x) = \begin{cases} 1 & \text{if x \in \mathbb{Q}} \\ -1 & \text{if x \not\in \mathbb{Q}} \end{cases}$ · 1 year, 9 months ago