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I know this is kind of minor. But I want to know if I understand this correctly. In "baby rudin", on page 42, is the condition

$$3^{-m}\lt \frac{\beta-\alpha}{6}$$

tight? I thought $$3^{-m}\lt \frac{\beta-\alpha}{4}$$ is sufficient, am I correct?

Thanks.

Edit: Okay, the background is: the Cantor set (i.e. the union of all intervals after repeatedly removing all the middle third interval) does not contain any point lying in the segment

$(\frac{3k+1}{3^m},\frac{3k+2}{3^m})$

And he was saying every segment $(\alpha, \beta)$ contains a segment of the form above, if

$$3^{-m}\lt \frac{\beta-\alpha}{6}$$

But I thought this condition is too loose.

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    It might help if you gave some background.2011-01-24
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    You could post more information. What are $m, \alpha$ and $\beta$ and how are they related? Without that, if $\beta=\alpha$ both claims are false. But it could well be that the first is tight and the second sufficient, as the second is looser and we do not know how you are using it.2011-01-24

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