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Show $x^2$ in the interval $(0,1/3]$ has no fixed points.

I understand that the range of that domain is always lower than $y=x$, but what is a proper way of showing this? $$\left(0,\frac13\right] \to \left(0,\frac19\right]$$

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    Funny looking intervals!2012-04-12
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    @lhf: I now have a pain in the neck, straining to tilt my head to the right...2012-04-12

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