Let $\Phi \subset V$ be a finite root system in a finite-dimensional real [vector space](/page/Vector%20Space) $V$, let $\Phi^+ \subset \Phi$ be a positive system, and let $\Delta \subset \Phi^+$ be the base of simple roots associated to $\Phi^+$. Then for every positive root $\gamma \in \Phi^+$, there exists a unique family of nonnegative integers $(n_\alpha)_{\alpha \in \Delta}$ such that

\begin{align*} \gamma = \sum_{\alpha \in \Delta} n_\alpha \alpha. \end{align*}