Definition:Nested Sequence

Definition
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).

Also known as
A nested sequence is a specific example of a chain (of sets) in which the underlying set forms a sequence.

Hence it is also a specific example of a nest.

Also see

 * Definition:Chain (Order Theory)