Definition:Strictly Positive/Real Number/Definition 2

Definition

The strictly positive real numbers, written $R_{>0}$, is the subset of $\R$ that satisfies the following:

$(\R_{>0} 1)$	$:$	Closure under addition	$\ds \forall x, y \in \R_{>0}:$	$\ds x + y \in \R_{>0} $
$(\R_{>0} 2)$	$:$	Closure under multiplication	$\ds \forall x, y \in \R_{>0}:$	$\ds xy \in \R_{>0} $
$(\R_{>0} 3)$	$:$	Trichotomy	$\ds \forall x \in \R:$	$\ds x \in \R_{>0} \lor x = 0 \lor -x \in \R_{>0} $

\((\R_{>0} 1)\)	$:$	Closure under addition	\(\ds \forall x, y \in \R_{>0}:\)	\(\ds x + y \in \R_{>0} \)
\((\R_{>0} 2)\)	$:$	Closure under multiplication	\(\ds \forall x, y \in \R_{>0}:\)	\(\ds xy \in \R_{>0} \)
\((\R_{>0} 3)\)	$:$	Trichotomy	\(\ds \forall x \in \R:\)	\(\ds x \in \R_{>0} \lor x = 0 \lor -x \in \R_{>0} \)