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I want to find examples of unbounded continuous function $f:Q\cap[0,1]\rightarrow R$
I am thinking $\frac{1}{1+n}$ may satisfy but not quite sure.
And if there are I want to see other examples too.
Thanks!

Kane
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  • $$\begin{split} \lim_{n\to1^-}\frac{1}{1+n}&=\frac{1}{2}\ \lim_{n \to 0^+} \frac{1}{1+n} &= 1 \end{split}$$

    Moreover $f(n) = \frac{1}{1+n}$ is monotonic on [0;1].

     – Tacet Nov 30 '14 at 18:58
  • Ok, then $n^2$ will do? – Kane Nov 30 '14 at 19:04
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    No! Why it should? Look at Hamou answer. – Tacet Nov 30 '14 at 19:15
  • Ok. I was stupid. I don't know why I came up with those. I wasn't able to find an example anyways but those are not. – Kane Nov 30 '14 at 19:33

1 Answers1

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Take $a\in [ 0,1]$ s.t $a\notin\Bbb Q $ and $ f(x)=\dfrac{ 1}{ x-a}$

Hamou
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