Let $R$ be a root system. Suppose $\alpha\in R$ and if for some $k \in \Bbb{R}$ we have $k\alpha\in R$ then how to prove $k=1,2,-1,-2,1/2,-1/2$? I just know $\frac{2(\alpha,\beta)}{<\alpha,\alpha>}$ will be an integer could any one help me why this term is bounded by $2$ above?
I am reading from this link I am at page 3