EDB — 1ZX

[1ZX] In an ordered field $F$ we call $P=\{x\in F:x\ge 0\}$ the set of positive (or zero) numbers; it satisfies the following properties: ¹

• $x,y\in P\Rightarrow x+y,x·y\in P$,

• $P\cap (-P)=\{0\}$ and

• $P\cup (-P)=F$.

vice versa if in a field $F$ we can find a set $P\subseteq F$ that satisfies them, then $F$ is an ordered field by defining $x\le y\iff y-x\in P$.