Nested Interval Property and Proof | Real Analysis

We introduce and prove the nested interval property, or nested interval theorem, or NIP, whatever you like to call it. This theorem says that, given a sequence of nested and closed intervals, that is, closed intervals J1, J2, J3, and so on such that each Jn contains Jn+1, this infinite sequence of nested intervals has a nonempty intersection. We prove this using the axiom of completeness and a supremum. #RealAnalysis

Real Analysis playlist:    • Real Analysis  
Real Analysis exercises:    • Real Analysis Exercises  

Supremum and Infimum:    • Definition of Supremum and Infimum of...  
Axiom of Completeness: (coming soon)

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