On the Number of Sum‐Free Sets

Cameron and Erdős have considered the question: how many sum‐free sets are contained in the first n integers;they have shown (personal communication) that the number of sum‐free sets contained within the integers {⅓ n , ⅓ n + 1, …, n } is c .2 n /2 . We prove that the number of sets contained within {l, 2, …,n} is o (2 n (½+ε) ) for every ε > 0.