Definition 13.1.5 (Order Complete). Let $(E, \le)$ be an ordered vector space, then $E$ is order complete if for any order bounded set $A \subset E$, $\sup (A)$ and $\inf (A)$ exist.
Definition 13.1.5 (Order Complete). Let $(E, \le)$ be an ordered vector space, then $E$ is order complete if for any order bounded set $A \subset E$, $\sup (A)$ and $\inf (A)$ exist.