Category:Definitions/Nested Sequences

This category contains definitions related to Nested Sequences.
Related results can be found in Category:Nested Sequences.

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 sequence 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).