Applications of the Nested Interval Theorem - 2

This is the second 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 Priyanka Vaideesh. 0:00 Introduction . 01:24 Definition of continuity . 05:10 Local preservation of the sign. 09:05 Global preservation of sign on an domain interval. 12:00 Intermediate value theorem. 15:20 Proof by the nested interval theorem (known as bisection method) 23:14 Use of nested interval theorem in proof. 30:40 Standard version of intermediate value theorem and proof.