Definition:Increasing Sequence of Sets

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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:

$\forall k \in \N: S_k \subseteq S_{k + 1}$

Then $\sequence {S_k}_{k \mathop \in \N}$ is an increasing sequence of sets (in $\SS$).


Also known as

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


Also see


Sources