Definition:Monotone Sequence of Sets
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Definition
Let $X$ be a set.
Let $\SS \subseteq \powerset X$ be a collection of subsets of $X$.
A monotone sequence of sets (in $\SS$) is a sequence $\sequence {A_n}_{n \mathop \in \N}$ in $\SS$, such that either:
- $\forall n \in \N: A_n \subseteq A_{n + 1}$
or:
- $\forall n \in \N: A_n \supseteq A_{n + 1}$
That is, such that $\sequence {A_n}_{n \mathop \in \N}$ is either increasing or decreasing
Also see
Sources
- 1970: Avner Friedman: Foundations of Modern Analysis ... (previous) ... (next): $\S 1.1$: Rings and Algebras
- 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.15$: Sequences