Let $\mathfrak{g}$ be finite-dimensional and semisimple over an algebraically closed field $k$ of characteristic zero, let $\mathfrak{h}\subset \mathfrak{g}$ be a Cartan subalgebra, and let $\Phi\subset \mathfrak{h}^*$ be the corresponding root system. For every root $\alpha\in\Phi$, the root space $\mathfrak{g}_\alpha$ is one-dimensional.