Definition:Strictly Negative

Let $$\left({R, +, \circ; \le}\right)$$ be an ordered ring whose zero is $$0_R$$.

Then $$x \in R$$ is strictly negative iff $$x \le 0_R$$ and $$x \ne 0_R$$.

The set of all strictly negative elements of $$R$$ is denoted:

$$\mathbf {Define:} \ R_-^* \ \stackrel {\mathbf {def}} {=\!=} \ \left\{{x \in R: x \ne 0 \land x \ne 0}\right\}$$