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## Diophantine numbers [closed]

A real number $x$ is defined to be diophantine if, for every $\epsilon>0$, there exists a constant $c_{\epsilon}$ such that

$$\left|x-\frac{a}{q}\right| \geq \frac{c_{\epsilon}}{|q|^{2+\epsilon}} \text{for every rational number} \frac{a}{q}$$

Show that the set $\{ x\in [0,1]: x\text{ is not diophantine}\}$ contains a thick subset of $[0,1]$.

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We don't like to be ordered to do things on MO. – Gerry Myerson Mar 6 2011 at 23:14
Homework in an analytic number theory class? – Mark Sapir Mar 6 2011 at 23:56
To expand slightly on Gerry's comment: the imperative form gives the impression that the question being asked has been set as an exercise, meaning that the answer/proof is known and that the person posting on MO has been asked to find the answer/proof as an exercise. If this is the case, this is not what MO should be used for. If this is not the case, then more explanation should be added as to how the question arose, and what has already been done to try and solve it. – Yemon Choi Mar 6 2011 at 23:59
@Mark: I suspect so, especially since the terminology "thick" has not been defined. – Yemon Choi Mar 7 2011 at 0:00
@Yemon: Then I suggest we close the question unless the author includes a motivation. I voted to close. – Mark Sapir Mar 7 2011 at 0:14
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