Proving the least upper bound property for real numbers

From the definition of the real number to the least upper bound property takes a good amount of work. In this video we go through the entire process of defining a least upper bound and proving that a certain construction actually gives us just that. We use the convergent sequence definition of Real Numbers that comes from Cantor.

The Extended Version of this video can be found here:    • Least Upper Bound Property (Extended)  

//Books
Maxwell Rosenlicht - Introduction to Analysis - https://amzn.to/3NFYiAC

Tom Apostol - Mathematical Analysis 2nd Edition - https://amzn.to/3mwxFlC

Walter Rudin - Principles of Mathematical Analysis 3rd Edition - https://amzn.to/3MDHUis



//Exercises
Finish showing that the Cauchy sequence definition of real numbers provides a field.


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0:00 Start
0:55 Partial Orderings and Least Upper Bounds
2:16 Total Orderings and Real Numbers
4:03 The LUB Algorithm
5:16 Square Root of 2
7:33 Real Distances
8:36 Proving the LUB Algorithm Works
9:50 Constructing a LUB
12:22 To Be Continued...