Cameron–Erdős conjecture

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

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

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