I'm doing a presentation on using probability to prove various results, and one of them is that given any set of natural numbers B, it contains a set A that is sum-free, i.e. no two elements in A sum to another element in A, such that [tex] |A| \geq \frac{|B|}{3}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Sumfree subsets

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