Limits of Sequences

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Introduction to Analysis › Limits of Sequences

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What term does the following define.

A sequence of sets $\begin{Bmatrix} I_n \end{Bmatrix}_{n\ \epsilon\ \mathbb{N}}$ is __________ if and only if $I_1\supseteq I_2\supseteq ...$ .

Nested

Increasing

Decreasing

Bounded

Unbounded

Explanation

This statement:

A sequence of sets $\begin{Bmatrix} I_n \end{Bmatrix}_{n\ \epsilon\ \mathbb{N}}$ is __________ if and only if $I_1\supseteq I_2\supseteq ...$

is the definition of nested.

This means that the sequence for all elements, for which belongs to the natural numbers, is considered a nested set if and only if the subsequent sets are subsets of it.

Other theorems in intro analysis build off this understanding.

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