Definition:Strictly Positive/Real Number/Definition 2

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Definition

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      \(\displaystyle \forall x \in \R:\) \(\displaystyle x \in \R_{>0} \lor x = 0 \lor -x \in \R_{>0} \)             


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