Definition:Decreasing Sequence of Sets

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 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 $\SS$).

Also known as

Some sources refer to such a sequence of sets as monotone decreasing.