Cauchy sequences, Cauchy criterion, convergence (example)

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Published on Jan 11, 2021

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In today's video we'll look at what it means for a sequence to be a Cauchy sequence! You'll also see how the convergence of a sequence is related to the Cauchy criterion, namely that every convergent sequence is also a Cauchy sequence. The reverse, however, does not necessarily hold true, as we'll see with a simple example. Subscribe for more videos like this: / @think_logic Share the video with a friend if it helped you: • Cauchy sequences, Cauchy criterion, conv... Timestamps: 0:00 - Intro 0:15 - graphical intuition 1:25 - definition of Cauchy sequence 2:42 - Cauchy sequences and convergence . Would you like to support my channel? - Here you can find my PayPal link: ????https://www.paypal.com/donate/?hosted... ????My book recommendations for studying physics???? 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 your physics studies. I was personally very happy 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 didn't use it that often, 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 study, 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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