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.
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Walter Rudin Principles of Mathematical Analysis 3rd Edition https://amzn.to/3MDHUis
Gerald Folland Real Analysis: Modern Techniques and Their Applications https://amzn.to/3JmK6Np

R. Shankar Principles of Quantum Mechanics https://amzn.to/40825xj
Tom Apostol Mathematical Analysis 2nd Edition https://amzn.to/3mwxFlC

//Reference for Cantor’s Work
https://www.ias.ac.in/article/fulltex...

//Exercises
Show that the elements of the Cantor set can be written in base3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.

//Watch Next
The Real Analysis Survival Guide    • The Real Analysis Survival Guide  
Mastering the Art of Reading a Proof: By Example    • Mastering the Art of Reading Proofs: ...  
Introduction to Control Theory    • Introduction to Control Theory  

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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?