What is Mathematics?

In this video I talk about an amazing book written by two legendary mathematicians. The book is called "What is Mathematics?" and it was written by Richard Courant and Herbert Robbins. I talk about various sections in this book and spend a lot of time talking about the Mathematical Analysis of Infinity. We discuss why there are just as many numbers in (0, 1) as there are real numbers. We also discuss why the rational numbers are countable and the real numbers are uncountable. I also go over the proof that (0,1) is uncountable(it's a beautiful proof by contradiction). Other topics explored in this video include continued fractions, deformations in topology, etc. This book covers A LOT of mathematics and I only briefly touch on some of the topics in this video. This is the book on amazon: https://amzn.to/3u7Ye4G The pencils I use in the video: https://amzn.to/3yr5MCs The paper I use in the video: https://amzn.to/3QLferc (the links above 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: https://www.facebook.com/themathsorcerer There are several ways that you can help support my channel:) Consider becoming a member of the channel: https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join My GoFundMe Page: https://www.gofundme.com/f/support-math-education-for-the-world My Patreon Page: https://www.patreon.com/themathsorcerer Donate via PayPal: https://paypal.com/donate/?cmd=_s-xclick&hosted_button_id=7XNKUGJUENSYU ************Udemy Courses(Please Use These Links If You Sign Up!)************* Abstract Algebra Course https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A Advanced Calculus Course https://www.udemy.com/course/advanced-calculusreal-analysis-with-the-math-sorcerer/?referralCode=0ABDD66D061D976EE232 Calculus 1 Course https://www.udemy.com/course/calculus-1-with-the-math-sorcerer/?referralCode=E853B70ED36571CA9768 Calculus 2 Course https://www.udemy.com/course/calculus-2-with-the-math-sorcerer/?referralCode=BAA5520B32FEA9827D54 Calculus 3 Course https://www.udemy.com/course/calculus-3-with-the-math-sorcerer/?referralCode=296462D1897904C4BEB3 Calculus 1 Lectures with Assignments and a Final Exam https://www.udemy.com/course/calculus-1-lectures-with-the-math-sorcerer/?referralCode=5D425153B63A8F506E30 Calculus Integration Insanity https://www.udemy.com/course/calculus-integration-insanity-with-the-math-sorcerer/?referralCode=D533EEE31F90EDDAFF93 Differential Equations Course https://www.udemy.com/course/differential-equations-with-the-math-sorcerer/?referralCode=4F0D91B41F7DACF4EC28 Differential Equations Lectures Course (Includes Assignments + Final Exam) https://www.udemy.com/course/differential-equations-lectures-with-the-math-sorcerer/?referralCode=89E6CCC307A7A8627CD6 College Algebra Course https://www.udemy.com/course/college-algebra-with-the-math-sorcerer/?referralCode=B2929EE97EF68DB9B69F How to Write Proofs with Sets Course https://www.udemy.com/course/how-to-write-proofs-in-set-theory-with-the-math-sorcerer/?referralCode=D503A7E3FB6916CF2D27 How to Write Proofs with Functions Course https://www.udemy.com/course/how-to-write-proofs-with-functions-with-the-math-sorcerer/?referralCode=DBACD59AB7B16D4707CD Trigonometry 1 Course https://www.udemy.com/course/trigonometry-1-with-the-math-sorcerer/?referralCode=79E02DDFD4106A909AF5 Trigonometry 2 Course https://www.udemy.com/course/trigonometry-2-with-the-math-sorcerer/?referralCode=7966E40F319B4FEF6535 Statistics with StatCrunch Course https://www.udemy.com/course/statistics-with-statcrunch-by-the-math-sorcerer/?referralCode=69B27AF43D10924FF63B Math Graduate Programs, Applying, Advice, Motivation https://www.udemy.com/course/math-graduate-programs-applying-advice-motivation/?referralCode=70A1CED973D7910E9161 Daily Devotionals for Motivation with The Math Sorcerer https://www.udemy.com/course/daily-math-devotionals-for-motivation-with-the-math-sorcerer/?referralCode=2653144E315A37A94B8C Thank you:)