= Root string
{title2=$S_{\alpha,\beta}=\Phi\cap(\beta+\mathbb Z\alpha)$}
A root string is the set $S_{\alpha,\beta}=\Phi\cap(\beta+\mathbb Z\alpha)$ for roots $\alpha,\beta$ of a <root system> $\Phi$. For nonproportional roots $\alpha$ and $\beta$ of a reduced crystallographic <root system>, the roots of the form $\beta+n\alpha$ form an unbroken <root string> $\beta-p\alpha,\ldots,\beta+q\alpha$, and $p-q=\langle\beta,\alpha^\vee\rangle$. The <root-string theorem> explains the endpoint relation. If $\beta=\pm\alpha$, zero is missing and this consecutive-string statement does not apply.
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