Sum-free set

Summary

A sum-free set is a subset $A$ of an abelian group that contains no solution of $x + y = z$ with $x, y, z \in A$. Equivalently, the sumset $A + A$ is disjoint from $A$. Sum-free sets are central in additive combinatorics and Ramsey theory. Schur's theorem says that the positive integers cannot be split into finitely many sum-free sets.