Applications of the Nested Interval Theorem - 3

This is the last of the series of 3 lectures on the applications of the nested interval theorem. The applications are:
1) Bolzano-Weierstrass Theorem on Bounded Sequences
2) The Intermediate Value Theorem
3) Bolzano's theorem on the boundedness of continuous functions on closed and bounded intervals.

Timestamp provided by Tamoghna Kar.
00:00 Introduction(Recall the definition of continuity and its geometric meaning, the notion of "locally boundedness")
04:46 Bolzano's theorem on the boundedness of continuous functions on closed and bounded
08:00 A continuous function is locally bounded
10:09 Pearl of wisdom: From local to global and back (subtle insight)
12:04 Recall: Archimedean Property
13:48 Proof of Bolzano's theorem on the boundedness of continuous functions on closed and bounded Intervals
22:31 Apply Nested Interval Theorem
30:34 Conclusion