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Proving the least upper bound property for real numbers
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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.
//Books
//Exercises
- Finish showing that the Cauchy sequence definition of real numbers provides a field.
//Watch Next
Real Analysis:
Control Theory:
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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...
//Books
//Exercises
- Finish showing that the Cauchy sequence definition of real numbers provides a field.
//Watch Next
Real Analysis:
Control Theory:
//Music Provided by Epidemic Sound
Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:
//Recording Equipment
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
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...
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