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How can I prove that the function $f$ defined by

$$f(x)=1/[1 + e^{1/\sin({n!{\pi}x})}] $$ Can be made discontinuous at any rational point in$[0,1]$ by a proper choice of $n$.

Plz help me with this.

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    How $f(x)$ depends on $n$? Or $\lim\limits_{n\rightarrow{\infty}}$ is omitted?2012-10-27

2 Answers 2