= Positive real number
{title2=$x\in\mathbb R,\quad x>0$}
A <positive real number> is a <real number> $x$ with $x>0$. Zero is excluded; allowing zero gives a <nonnegative real number>. Both $1/2$ and $\sqrt2$ are positive.
The sum, product, and reciprocal of positive <real numbers> are positive. Consequently the <positive real numbers> form a <group> under multiplication, and the <natural logarithm> converts that multiplication into <addition>: $\log(xy)=\log x+\log y$. Positivity is also the domain restriction that makes the real <logarithm> well-defined.
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