Real Numbers: Lecture 9 (Nested Interval Theorem)

We prove the nested interval theorem and discuss some examples and counterexamples. 00:00 Introduction 01:09 Statement of the result 03:06 Concept involved in the theorem. 08:41 Proof 18:49 Examples: (1) Jn=[0,1/n], (2) In=[0,1+1/n]. 20:41 Counter examples 24:21 Uniqueness part. 31:26 Remark on the theorem.