Uploaded April 2023 | Updated September 2026, 1 week ago
Here we dissect a theorem statement about convergent sequences from Rudin's Principles of Mathematical Analysis (a.k.a. Baby Rudin). There is a lot to unpack here, including some allusions to Topology.
//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.
amzn.to/3NFYiAC
Walter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUis
Gerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6Np
R. Shankar - Principles of Quantum Mechanics - amzn.to/40825xj
Tom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC
//Reference for Cantor’s Work
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 youtu.be/v5rD0B-zfXw
Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQ
Introduction to Control Theory 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:
epidemicsound.com/referral/644nao
//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
Blue Yeti Microphone: amzn.to/3I1y88N
Yeti Nano Microphone: amzn.to/3I1mriA
SanDisc 256GB SD Card: amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: amzn.to/3xvB9cN
Neewer 18 inch Ring Light: amzn.to/2ZvgCsc
Camera Power Adapter: 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?
Here we dissect a theorem statement about convergent sequences from Rudin's Principles of Mathematical Analysis (a.k.a. Baby Rudin). There is a lot to unpack here, including some allusions to Topology.
//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.
amzn.to/3NFYiAC
Walter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUis
Gerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6Np
R. Shankar - Principles of Quantum Mechanics - amzn.to/40825xj
Tom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC
//Reference for Cantor’s Work
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 youtu.be/v5rD0B-zfXw
Mastering the Art of Reading a Proof: By Example youtu.be/WPWf_s6Q1QQ
Introduction to Control Theory 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:
epidemicsound.com/referral/644nao
//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
Blue Yeti Microphone: amzn.to/3I1y88N
Yeti Nano Microphone: amzn.to/3I1mriA
SanDisc 256GB SD Card: amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: amzn.to/3xvB9cN
Neewer 18 inch Ring Light: amzn.to/2ZvgCsc
Camera Power Adapter: 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?
