Definition:Strictly Positive

Definition
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:


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