Real Numbers: Lecture 2 (UpperBounds2)

This is the second of the series on upper and lower bounds. We introduce LUB and GLB. We look at some examples. The next in the series will be on the LUB property of R. It is best if you watch it in small group and at each P-R-P, you pause the video and discuss. This is what happens in my classrooms. 0:00 Introduction 3:08 Revision of previous lecture 4:11 Upper and lower bound for set A and -A 8:41 Observation for upper bound in open interval 12:46 Upper bounds in different types of intervals 29:06 Definition 1 of least upper bound 31:24 Revisiting the earlier examples for lub 33:02 Uniqueness of lub 37:04 Definition of glb and revisiting the earlier examples for glb 39:44 Sets not bounded above and not bounded below 43:08 Definition 2 for LUB 43:50 Equivalence of Definitions 1 and 2. 51:31 LUB of a finite set 57:35 The relation between the LUB and GLB of of the sets A and -A. 1:04:46 Exercise