Analysis problem

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November 11th 2008, 10:34 AM
AlexHall

Analysis problem

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

If the function http://alt1.mathlinks.ro/latexrender...7f95476ecc.gif is continuous in every irrational number x then f is continuous at every number.
November 11th 2008, 11:57 AM
ThePerfectHacker

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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