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**ramdayal9** Let $\displaystyle \Omega$ denote the set of numbers $\displaystyle x \in [0,1]$ such that there exist infinitely many

rationals $\displaystyle \frac{p}{q}$, with p and q coprime, with the property

$\displaystyle |x-\frac{p}{q}|<\frac{1}{q^3}$. Show that $\displaystyle \Omega$ has measure 0.

I think I should use the Borel Cantelli Lemma for this, however I am struggling to think of a suitable set An so that limsupAn= $\displaystyle \Omega$. Can you help me try to find a suitable set?