Let $G$ be a group and $\leq$ be an order. $G$ is ordered by $\leq$ if multiplication preserves the order, i.e. for all $a$, $b$, $x\in G$,
\[a\leq b \enspace\rimp\enspace ax\leq bx \,\land\, xa\leq xb.\]
Let $G$ be a group and $\leq$ be an order. $G$ is ordered by $\leq$ if multiplication preserves the order, i.e. for all $a$, $b$, $x\in G$,
\[a\leq b \enspace\rimp\enspace ax\leq bx \,\land\, xa\leq xb.\]