\begin{definition}[Definition:Comparable Filters on Set]
Let $S$ be a set.
Let $\powerset S$ be the power set of $S$.
Let $\FF, \FF' \subset \powerset S$ be two filters on $S$.
$\FF$ and $\FF'$ are '''comparable''' {{iff}} one is finer (or coarser) than the other.
\end{definition}