### 3.7.227. Schur number

Denotes that a constraint was used for solving Schur problems. Given a non-negative integer $k$, the Schur number $S\left(k\right)$ is the largest integer $n$ for which the set $\left\{1,2,\cdots ,n\right\}$ can be partitioned into $k$ sets ${S}_{1},{S}_{2},\cdots ,{S}_{k}$ such that $\forall i\in \left[1,k\right]:i\in {S}_{i}⇒i+i\notin {S}_{i}$.