# Cameron–Erdős conjecture

In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in $|N|=\{1,\ldots,N\}$ is $O\left({2^{N/2}}\right).$

The sum of two odd numbers is even, so a set of odd numbers is always sum-free. There are $\lceil N/2\rceil$ odd numbers in |N|, and so $2^{N/2}$ subsets of odd numbers in |N|. The Cameron–Erdős conjecture says that this counts a constant proportion of the sum-free sets.

The conjecture was stated by Peter Cameron and Paul Erdős in 1988.[1] It was proved by Ben Green[2] and independently by Alexander Sapozhenko[3][4] in 2003.