Introduction to Analysis : Limits of Sequences

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Example Questions

Example Question #1 : Limits Of Sequences

What term does the following define.

A sequence of sets  is __________ if and only if .

Possible Answers:

Increasing

Decreasing

Nested

Unbounded

Bounded

Correct answer:

Nested

Explanation:

This statement:

A sequence of sets  is __________ if and only if 

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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