View source for Sum-free set

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''of an Abelian group or semigroup $M$''

A subset $S \subset M$ with the property that no element of $S$ is equal to a sum of two elements of $S$.  It is known that in general a subset of $M$ of size $n$ contains a sum-free subset of order $> \frac27 n$.  The set of odd numbers in $\{1,\ldots,n\}$ is a sum-free set of order $\frac12 n$.

The [[Cameron–Erdős conjecture]], proved by Ben Green in 2003, asserts that the set $\{1,\ldots,n\}$ contains $O\left({2^{n/2}}\right)$ sum-free sets.

====References====
* Guy, Richard K. ''Unsolved problems in number theory'' (3rd ed.) Springer-Verlag (2004) {{ISBN|0-387-20860-7}} {{ZBL|1058.11001}}