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Office_Shredder

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I looked around and found a slightly better result that there is always a sum free subset of B of magnitude [tex] |A| \geq \frac{|B+2|}{3}[/tex]. I've been trying to construct an example for B that gets this bound or close to it, but it's not working out so well. Does anyone know of a good example of such a set, or if there's a better bound that's known?