Definition 3

In an ordered group $G$, any element $x$ such that $0 \leq x$ (resp. $x \leq 0$) is called a positive (resp. negative) element.

Note that $0$ is the only element which is both positive and negative ; any element $x$ such that $0 < x$ (resp. $x < 0$) is called strictly positive (resp. strictly negative).