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: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC
Supremum and Infimum: https://youtu.be/QRGIhqz9vh4
Axiom of Completeness: (coming soon)
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