Definition:Dedekind Complete Set

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Then $\left({S, \preceq}\right)$ is Dedekind complete iff every non-empty subset of $S$ that is bounded above admits a supremum (in $S$).

Also see

 * Dedekind Completeness is Self-Dual
 * Dedekind completion