The main result of this session is that an interval of the form [a,b] is connected. As many students are not confident of the LUB (aka supremum) etc., we review it quickly and embark on a proof. The proof is incomplete. After watching the video, can you find why? In the beginning of the next lecture, this gap will be taken care of!
Timestamp: Argha Mazumdar and Ishwarya
0:00 Introduction
3:24 Recalling the definition
4:22 R* is not connected
6:36 Q is not connected
9:52 Z is not connected
11:14 If A be a subset of R which is not an interval then A is not connected
18:50 Theorem: The closed and bounded interval [a,b] is connected in R
19:53 Quick Recap of Least upper bound definition
25:37 Proof of the Theorem
45:44 Summary of the proof
