The Nested Interval Theorem

Published: 07 December 2020
on channel: Elliot Nicholson

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The nested interval theorem is a theorem in real analysis.

It states that if you have a sequence of closed nested intervals within the real line, then their intersection is non-empty.

In this video I explain this in more details.

I also give examples and explain how it doesn’t hold true in the rationals or for open nested intervals.

Finally we use the completeness axiom of the real numbers to prove the theorem.

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