Let $\Phi$ be a finite irreducible root system in a real Euclidean [vector space](/page/Vector%20Space) $E$ with inner product $(\cdot,\cdot)$, let $\Delta \subset \Phi$ be a base of simple roots, and let $\Phi^+$ be the corresponding set of positive roots. Equip the root lattice with the root order determined by $\Delta$: for $\mu,\nu \in \operatorname{span}_{\mathbb{Z}}(\Delta)$, write $\mu \le \nu$ if $\nu-\mu$ is a non-negative integer linear combination of elements of $\Delta$. Then there exists a unique root $\theta \in \Phi^+$ such that $\gamma \le \theta$ for every $\gamma \in \Phi^+$.