\begin{definition}[Definition:Element is Way Below]
Let $\left({S, \preceq}\right)$ be an ordered set.
Let $x, y \in S$.
Then $x$ '''is way below''' $y$, denoted $x \ll y$, {{iff}}
:for every directed subset $D$ of $S$
::if $D$ admits a supremum and $y \preceq \sup D$
::then there exists $d \in D$ such that $x \preceq d$
\end{definition}