Category:Definitions/Nested Sequences

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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:

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


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

Then $\family {S_k}_{k \mathop \in \N}$ is a nested sequence (of sets).

Pages in category "Definitions/Nested Sequences"

The following 4 pages are in this category, out of 4 total.