# Category:Decreasing Sequences of Sets

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This category contains results about **Decreasing Sequences of Sets**.

Definitions specific to this category can be found in Definitions/Decreasing Sequences of Sets.

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 $\SS$)**.

## Subcategories

This category has only the following subcategory.

## Pages in category "Decreasing Sequences of Sets"

The following 9 pages are in this category, out of 9 total.

### L

- Limit of Decreasing Sequence of Left Half-Open Intervals with Lower Bound Converging to Upper Bound
- Limit of Decreasing Sequence of Sets is Intersection
- Limit of Decreasing Sequence of Unbounded Below Closed Intervals
- Limit of Decreasing Sequence of Unbounded Below Closed Intervals with Endpoint Tending to Negative Infinity
- Limit of Tail of Decreasing Sequence of Sets