Limits of Sequences - Introduction to Analysis

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Question

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 $I_1\supseteq I_2\supseteq ...$ .

Answer

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.

Compare your answer with the correct one above

Question

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 $I_1\supseteq I_2\supseteq ...$ .

Answer

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.

Compare your answer with the correct one above

Question

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 $I_1\supseteq I_2\supseteq ...$ .

Answer

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.

Compare your answer with the correct one above

Question

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 $I_1\supseteq I_2\supseteq ...$ .

Answer

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.

Compare your answer with the correct one above

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