The Riemann Rearrangement Theorem // I can make this sum anything I want

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. https://amzn.to/3NFYiAC 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/fulltext/reso/019/11/0977-0999 //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 The Real Analysis Survival Guide https://youtu.be/v5rD0B-zfXw Mastering the Art of Reading a Proof: By Example https://youtu.be/WPWf_s6Q1QQ Introduction to Control Theory https://youtu.be/0v4WFmOm764 //Music Provided by Epidemic Sound Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel: https://www.epidemicsound.com/referral/644nao //Recording Equipment Canon SL3: https://amzn.to/3nZ11KU Canon T6i: https://amzn.to/3FUpkQh Rode VideoMic: https://amzn.to/3lhldGa Blue Yeti Microphone: https://amzn.to/3I1y88N Yeti Nano Microphone: https://amzn.to/3I1mriA SanDisc 256GB SD Card: https://amzn.to/3E3LOOr Neewer 5600K USB LED Lights: https://amzn.to/3xvB9cN Neewer 18 inch Ring Light: https://amzn.to/2ZvgCsc Camera Power Adapter: https://amzn.to/3D3upUu 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?