Ordered Field

An ordered field is a Field that has Order $<$ satisfying these additional properties:

1. $\mathrm{\forall }x,y,z\in \mathbb{F}$, if $x<y$ then $x+z<y+z$ (additive preservation of $<$)
2. $\mathrm{\forall }x,y\in \mathbb{F}$ where $x,y>0$, then $xy>0$ (multiplicative preservation of $<$)