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The Riemann Rearrangement Theorem // I can make this sum anything I want
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Here we investigate the Riemann Rearrangement Theorem from the 19th century. Analysis was changed forever after this discovery.
//Books
A great companion text to Rudin is Maxwell Rosenlicht's Introduction to Analysis. The explanations are a lot clearer and the book is under $20.
//Reference for Cantor’s Work
//Exercises
- Show that the elements of the Cantor set can be written in base-3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.
//Watch Next
//Music Provided by Epidemic Sound
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//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 Introduction
0:40 Anticipating Topology
1:48 Proof of Part A
3:53 Can a sequence converge to more than one point?
5:17 Proof of Part B
8:21 Using a Theorem Backwards
8:47 Functional Analysis Example
10:28 What about a PROOF?
//Books
A great companion text to Rudin is Maxwell Rosenlicht's Introduction to Analysis. The explanations are a lot clearer and the book is under $20.
//Reference for Cantor’s Work
//Exercises
- Show that the elements of the Cantor set can be written in base-3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.
//Watch Next
//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 Introduction
0:40 Anticipating Topology
1:48 Proof of Part A
3:53 Can a sequence converge to more than one point?
5:17 Proof of Part B
8:21 Using a Theorem Backwards
8:47 Functional Analysis Example
10:28 What about a PROOF?
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