f: (0,+inf)->R and(adsbygoogle = window.adsbygoogle || []).push({});

f(x) is

0 if x is irrational

1/n if x is rational (n is positive integer)

For each rational and irrational, i want to show continuity/discontinuity of f

Intuitively, i think at each rational f is discontinuous, and at each irrational f is continuous,

but i cannot figure out how should i apply differentiability to this problem...

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# Continuity proved by differentiation

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