I just spent about an hour going through the proof that f(x) = 1/x is continous at every point in R\{0}, and I'm still not completely sure if I understood the proof. I wonder if someome could perhaps present a more elegant and easy way to proove this, or is this the only way? I should actually present the proof here, but I'm interested in how someome else would proove that.(adsbygoogle = window.adsbygoogle || []).push({});

P.S. If there exists some proof using limits, I'm not really interested in it, since the textbook defines continuity of a function without using limits.

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# Proof of continuity of f(x) = 1/x

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