Does anyone have a proof for this? Consider the function:
$f:\mathbb R \rightarrow \mathbb R $
defined by:
$f(x) = 0$ if $x\notin \mathbb Q$
$f(x) = 1/n$ if $x\in \mathbb Q $\ {$0$}
$f(x) = 0$ if $x=0$
Prove that f is continuous at ever irrational number and discontinuous at every rational number.