# 2016-7 Sum-free

For a set $$A \subset \mathbb{R}$$, let $$f(A)$$ be the size of the largest set $$B \subset A$$ such that $$(B+B) \cap B = \emptyset$$. For a positive integer $$n$$, let $$f(n) = \min_{0 \notin A, |A|=n} f(A)$$. Prove that $$f(n) \geq n/3$$.

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