Bolzano-Weierstrass theorem (EASILY explained!)
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In today's video we look at one of the most important theorems in analysis, namely the Bolzano-Weierstrass theorem. It states that every bounded sequence has at least one convergent subsequence! In this video I explain the statement of the Bolzano-Weierstrass theorem and in the next video I will show you how to prove this theorem. Subscribe for more videos like this: / @think_logic Share the video with a friend if it helped you: • Bolzano-Weierstrass theorem (EASY... Timestamps: 0:00 - Intro 0:15 - Partial episodes 1:45 - Bolzano-Weierstrass theorem . Would you like to support my channel? - Here you can find my PayPal link: ????https://www.paypal.com/donate/?hosted... ????My book recommendations for physics studies???? If you buy one of my book recommendations via the Amazon links below, I will receive a small commission as an Amazon partner. These two textbooks are the standard literature for starting physics studies. I was personally very satisfied with the second book in the series on electricity and optics, and I still use it often today to look up certain topics. I only bought the first book at the end of the first semester, so I haven't read it that often. used, but it helped me a lot with certain topics for exam preparation! The books are also suitable for preparing for your studies before you start, especially since there are tasks at the end of each chapter, and the solutions to these tasks are also at the back of the book. (I would probably skip the first chapter of the book Experimental Physics 1) ▶︎ Experimental Physics 1: Mechanics & Heat by Wolfgang Demtröder Amazon link: https://amzn.to/3DQBADP ▶︎ Experimental Physics 2: Electricity and Optics by Wolfgang Demtröder Amazon link: https://amzn.to/3DYgnaX After the first year of your studies, you continue with in-depth courses on theoretical mechanics, quantum mechanics and electrodynamics & statistical physics (thermodynamics). My book recommendations on these topics are partly in German and partly in English. This is because sooner or later (at the latest in the master's program) all lectures are held in English. I have also had very good experiences with all of these books myself! ▶︎ Classical Mechanics by John R. Taylor Amazon link: https://amzn.to/3r5Eixw ▶︎ Modern Quantum Mechanics by JJ Sakurai Amazon link: https://amzn.to/3UFvJa9 I mainly used this book for my first course on quantum mechanics and was very satisfied. ▶︎ Introduction to Quantum Mechanics by David J. Griffiths Amazon link: https://amzn.to/3BMZc9w As an alternative to Sakurai's book, I also ordered this book and can definitely recommend it. All the important topics are covered, but I would tend to go for the other option. ▶︎ Introduction to Electrodynamics by David J. Griffiths Amazon link: https://amzn.to/3LIjPbw Thanks for watching!
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