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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
2 years, 1 month 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 - 2 years, 1 month ago

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That's the exact correct answer!

Hobart Pao - 2 years, 1 month ago

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