# Serial Para Activar Office 2019l

Serial Para Activar Office 2019l

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Origin of the non-reduced root system

The following part is copied from this paper:

The nonreduced root system $\{\alpha \subseteq \Delta\}$ is defined to be the root system with the following
properties:
(a) $\alpha$ is a basis for the root space $V_\alpha$.
(b) If $\beta$ is a non-negative root, then $\alpha + \beta$ is a root.
(c) If $\alpha$ is a non-negative root and $\beta$ is a negative root, then $\alpha + \beta$ is a root.
(d) $\alpha + \beta$ is a root if and only if $\alpha + \beta$ is a non-negative root.

When I was reading out this page, I found it difficult to understand how is the phrase "let $\alpha$ be a non-negative root" appeared. I thought it should read "let $\alpha$ be a negative root," but the phrase in the page does not match with this.
Could someone enlighten me?

A:

The term $\alpha$ in this setting is not a vector. Rather, it’s a root. The restriction it’s a non-negative root is part of the definition. As Ross says, this is trying to make clear that roots are indeed non-negative vectors.

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