An Introduction to Naive Set Theory, Cantor's Theorem, Russell's Paradox & the History of Set Theory

In this video, I introduce Naive Set Theory from a productive conceptual understanding. I also prove Cantor's Theorem and Russell's Paradox to convey historical significance. Any feedback on how these videos can be improved would be great. I will be constantly updating these videos to ensure that everything is accurate. Thank you all for being such a great community. All content is released under Creative Commons "No Rights Reserved", so please feel free to use this video however you want. My name is Kody Amour, and I teach free undergraduate mathematics courses on YouTube. I'm currently developing three YouTube courses simultaneously: Discrete Math, Linear Algebra, Real Analysis, Topology, Number Theory and Complex Analysis. These courses correspond to playlists that I am constructing indefinitely. You have already given me a view and your watch time, which means a lot to me already. Your participation in this community contributes to exponential growth of this channel. If you'd like to give even more than you already have, please like, subscribe, share on a math SubReddit, comment, ring the bell, etc... **Please only give if you have the financial ability to do so** Patreon: https://www.patreon.com/amourlearning (Seriously - Thank you) ------------------------------------------------------------------------------------------------------------------- Credit to all of the authors of all of the resources below that greatly helped influence this video. Free open-access online math textbooks (I only use textbooks from this resource, since everything is free for my students): https://aimath.org/textbooks/approved-textbooks/ A free in-depth tutorial for SageMath: https://doc.sagemath.org/html/en/tutorial/ Learn LaTeX in 30 minutes: https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes ------------------------------------------------------------------------------------------------------------------- My favorite math-oriented YouTube channels (in no particular order): Aleph 0: https://www.seevid.ir/fa/result?ytch=UCzBjutX2PmitNF4avysL-vg The Bright Side of Mathematics: https://www.seevid.ir/fa/result?ytch=UCdwo4k1RQHTcq_-WS7Cazqg Math Visualized: https://www.seevid.ir/fa/result?ytch=UCnym_SvWIt_VfycYNt105aQ Insights into Mathematics: https://www.seevid.ir/fa/result?ytch=UCXl0Zbk8_rvjyLwAR-Xh9pQ ScienceClic English: https://www.seevid.ir/fa/result?ytch=UCWvq4kcdNI1r1jZKFw9TiUA Stand-up Maths: https://www.seevid.ir/fa/result?ytch=UCSju5G2aFaWMqn-_0YBtq5A Zach Star: https://www.seevid.ir/fa/result?ytch=UCpCSAcbqs-sjEVfk_hMfY9w Numberphile: https://www.seevid.ir/fa/result?ytch=UCoxcjq-8xIDTYp3uz647V5A 3Blue1Brown: https://www.seevid.ir/fa/result?ytch=UCYO_jab_esuFRV4b17AJtAw MIT OpenCourseWare: https://www.seevid.ir/fa/result?ytch=UCEBb1b_L6zDS3xTUrIALZOw Khan Academy: https://www.seevid.ir/fa/result?ytch=UC4a-Gbdw7vOaccHmFo40b9g PBS Infinite Series: https://www.seevid.ir/fa/result?ytch=UCs4aHmggTfFrpkPcWSaBN9g Lex Fridman: