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