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

Note by Hobart Pao 1 year, 11 months ago

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\[f : \mathbb{R} \to \mathbb{R}, \forall x f(x) = \begin{cases} 1 & \text{if $x \in \mathbb{Q}$} \\ -1 & \text{if $x \not\in \mathbb{Q}$} \end{cases}\] – Ivan Koswara · 1 year, 11 months ago

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@Ivan Koswara – That's the exact correct answer! – Hobart Pao · 1 year, 11 months ago

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TopNewest\[f : \mathbb{R} \to \mathbb{R}, \forall x f(x) = \begin{cases} 1 & \text{if $x \in \mathbb{Q}$} \\ -1 & \text{if $x \not\in \mathbb{Q}$} \end{cases}\] – Ivan Koswara · 1 year, 11 months ago

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– Hobart Pao · 1 year, 11 months ago

That's the exact correct answer!Log in to reply