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Math Help - Analysis problem

  1. #1
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    Analysis problem

    I need to show if the following is true or false.

    If the function is continuous in every irrational number x then f is continuous at every number.
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  2. #2
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    Let x\in \mathbb{Q} and write x = \frac{p}{q} where \gcd(q,|p|)=1 with q>0. Then define f(x) = \tfrac{1}{q} and f(\alpha) = 0 if \alpha \in \mathbb{R} - \mathbb{Q}. It turns out that f is continous at all the irrational points and discontinous at all the rational points.
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