# Definition:Strictly Positive/Real Number/Definition 2

The strictly positive real numbers, written $R_{>0}$, is the subset of $\R$ that satisfies the following:
 $(\R_{>0} 1)$ $:$ Closure under addition $\displaystyle \forall x, y \in \R_{>0}:$ $\displaystyle x + y \in \R_{>0}$ $(\R_{>0} 2)$ $:$ Closure under multiplication $\displaystyle \forall x, y \in \R_{>0}:$ $\displaystyle xy \in \R_{>0}$ $(\R_{>0} 3)$ $:$ Trichotomy $\displaystyle \forall x \in \R:$ $\displaystyle x \in \R_{>0} \lor x = 0 \lor -x \in \R_{>0}$