Definition:Strictly Positive

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

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

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

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