modestoraton
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If i have a measurable set with positive measure, how do I prove that there are 2 elements who's difference is in Q~{0} (aka a rational number that isn't 0.
Proving the Existence of Rational Differences in a Measurable Set
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Hi modestoraton! 
Let M is measurable such that there are no two elements who's differences are in [itex]\mathbb{Q}\setminus \{0\}[/itex]. Let [itex]M_n=M\cap[n,n+1][/itex].
Then perhaps you could evaluate the sum
[tex]\lambda\left(\bigcup_{q\in\mathbb{Q}\cap[-1,1]}{q+M_n}\right)[/tex]
and show that Mn has measure zero.
Let M is measurable such that there are no two elements who's differences are in [itex]\mathbb{Q}\setminus \{0\}[/itex]. Let [itex]M_n=M\cap[n,n+1][/itex].
Then perhaps you could evaluate the sum
[tex]\lambda\left(\bigcup_{q\in\mathbb{Q}\cap[-1,1]}{q+M_n}\right)[/tex]
and show that Mn has measure zero.
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modestoraton
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Thank you so much.