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
- 1951: J.C. Burkill: The Lebesgue Integral ... (previous) ... (next): Chapter $\text {I}$: Sets of Points: $1 \cdot 1$. The algebra of sets
- 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: Definition $15.4$