I am asked to prove:
"A set of integers $A$ is called sum-free if $a,b\in A \implies a+b \notin A$. Show that $\{1, 2, \ldots, 14 \}$ cannot be divided into three sum-free subsets."
Together with a sum-free partition of $\{1, 2, \ldots ,13 \}$, this is equivalent to $f(3)=13$, where $f$ denotes the Schur numbers. One valid partition is $\{2, 3, 11, 12\}, \{5,6,8,9\}, \{1,4,7,10,13\}$. I am unsure how to prove the first part.