Uploaded March 2023 | Updated September 2026, 2 days ago
Infinity is hard to understand, and Cantor, who introduced it, was ridiculed for it.
//Books
David Burton - History of Mathematics - amzn.to/3mrp8DU
Maxwell Rosenlicht - Introduction to Analysis - 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
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//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
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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
1:16 Kronecker on Cantor
2:03 How did Cantor get here?
6:08 Uncountability of Perfect Sets
10:14 What are Perfect Sets anyway?
11:37 Cantor's set
14:14 Wrap Up!
Infinity is hard to understand, and Cantor, who introduced it, was ridiculed for it.
//Books
David Burton - History of Mathematics - amzn.to/3mrp8DU
Maxwell Rosenlicht - Introduction to Analysis - 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
1:16 Kronecker on Cantor
2:03 How did Cantor get here?
6:08 Uncountability of Perfect Sets
10:14 What are Perfect Sets anyway?
11:37 Cantor's set
14:14 Wrap Up!
