\begin{definition}[Definition:Decreasing Sequence of Sets]
Let $S$ be a set.
Let $\SS = \powerset S$ be the power set of $S$.
Let $\sequence {S_k}_{k \mathop \in \N}$ be a nested sequence of subsets of $S$ such that:
:$\forall k \in \N: S_k \supseteq S_{k + 1}$
Then $\sequence {S_k}_{k \mathop \in \N}$ is a '''decreasing sequence of sets (in $\SS$)'''.
\end{definition}