- #1

WWGD

Science Advisor

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2019 Award

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## Main Question or Discussion Point

Hi, let E be a measurable subset of the Real line with m(E)>1 . I want to show

there are x,y in E so that x-y is in ## \mathbb Z-{0} ##. My idea is to restrict the

quotient ## \mathbb R / \mathbb Z |_E ##. This quotient cannot be contained in

[0,1], since m([0,1])=1 and m(E)>1. From this I want to show that there must be

more than one representative of each clase of the quotient in E , but I am having

trouble tightening up the argument. Any ideas?

Thanks.

there are x,y in E so that x-y is in ## \mathbb Z-{0} ##. My idea is to restrict the

quotient ## \mathbb R / \mathbb Z |_E ##. This quotient cannot be contained in

[0,1], since m([0,1])=1 and m(E)>1. From this I want to show that there must be

more than one representative of each clase of the quotient in E , but I am having

trouble tightening up the argument. Any ideas?

Thanks.