we know that A Set $S$ together with a relation $\ge$ which is both $transitive$ and $reflexive$ such that for any two elements a,b in $S$, there exists another element c in $S$ with c $\ge$ a and c $\ge$ b In this case, the relation $\ge$ is said to "direct" the set.
But can we call A Set $S$ is A FULL directed Set : If Every subset From $S$ is a directed Set?
I need an example of a directed set but it is not A Full directed one.