Definition:Nested Sequence

Definition
Let $\left \langle {S_k}\right \rangle$ be a sequence of sets 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 $\left \langle {S_k}\right \rangle$ is a nested sequence of sets.