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In this video I will show you a legendary book on mathematical analysis and then we will do some mathematics from this book. The book is called Mathematical Analysis and it was written by Tom Apostol. After discussing the book we will very a statement that is given in the text without proof. The statement has to do with two repeated series that converge but are not equal. The approach we take is a simple one in that we don't assume any prior knowledge. 0:00 The Mysterious Holes 0:29 Introduction 1:12 The Book 6:49 Repeated Series Here are a few copies of the book. This is an older edition https://amzn.to/3eyRMzl This is the 2nd edition https://amzn.to/3gf2k7e This is an import version https://amzn.to/3TjUqry (these are my affiliate links) If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com Free Homework Help : https://mathsorcererforums.com/ My FaceBook Page: / themathsorcerer There are several ways that you can help support my channel:) Consider becoming a member of the channel: / @themathsorcerer My GoFundMe Page: https://www.gofundme.com/f/support-ma... My Patreon Page: / themathsorcerer Donate via PayPal: https://paypal.com/donate/?cmd=_s-xcl... ***********Udemy Courses(Please Use These Links If You Sign Up!)************ Abstract Algebra Course https://www.udemy.com/course/abstract... Advanced Calculus Course https://www.udemy.com/course/advanced... Calculus 1 Course https://www.udemy.com/course/calculus... Calculus 2 Course https://www.udemy.com/course/calculus... Calculus 3 Course https://www.udemy.com/course/calculus... Calculus 1 Lectures with Assignments and a Final Exam https://www.udemy.com/course/calculus... Calculus Integration Insanity https://www.udemy.com/course/calculus... Differential Equations Course https://www.udemy.com/course/differen... Differential Equations Lectures Course (Includes Assignments + Final Exam) https://www.udemy.com/course/differen... College Algebra Course https://www.udemy.com/course/college-... How to Write Proofs with Sets Course https://www.udemy.com/course/how-to-w... How to Write Proofs with Functions Course https://www.udemy.com/course/how-to-w... Trigonometry 1 Course https://www.udemy.com/course/trigonom... Trigonometry 2 Course https://www.udemy.com/course/trigonom... Statistics with StatCrunch Course https://www.udemy.com/course/statisti... Math Graduate Programs, Applying, Advice, Motivation https://www.udemy.com/course/math-gra... Daily Devotionals for Motivation with The Math Sorcerer https://www.udemy.com/course/daily-ma... Thank you:)