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  "body": "\n## Summary\n\nA sum-free set is a subset $A$ of an abelian group that contains no solution of $x + y = z$ with $x, y, z \\in A$.\nEquivalently, the [[sumset|XNBN31HQWB]] $A + A$ is disjoint from $A$.\nSum-free sets are central in [[additive combinatorics|3NM362A2JG]] and [[Ramsey theory|G5TWXV565S]].\n[[Schur's theorem|V6XJQXZ7E8]] says that the positive integers cannot be split into finitely many sum-free sets.\n\n## Explanations\n\n### L1 human\n\nA set of numbers is sum-free if adding two of its members, possibly the same one twice, never gives a member.\nThe odd numbers are sum-free, because two odd numbers add up to an even number.\nThe set $\\set{6, 7, 8, 9, 10}$ is sum-free too, because every sum of two of its members is at least $12$.\nThe set $\\set{1, 2, 3}$ is not, since $1 + 2 = 3$.\n",
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