Imagine that you own a hotel. Your hotel has infinitely many rooms stretching down an infinite hallway—this is Hotel Infinity. Sometimes people call this Hilbert’s Hotel, after German mathematician David Hilbert. In this episode of "Mind-Bending Math: Riddles and Paradoxes", you will learn about the beginning of infinity, in all of its strange, paradoxical glory. As you will see, infinity introduces some really serious mathematical questions. Presented by David Kung Learn more about math paradoxes at www.wondrium.com/youtube 0:00 Conceptualizing Infinity 1:50 Imagining Infinity as a Hotel 4:30 What Happens If Infinitely Many New Guests Arrive and Hotel Infinity Has No Vacancies? 6:27 What If Two Busses Pulled Up, Each With Infinitely Many People On It? 6:35 What If Infinitely Many Busses Pulled Up With Infinitely Many People? 10:35 Relationship Between Prime Numbers and Infinity 13:45 Unique Prime Factorization 15:00 How Can the Hotel Infinite Accommodate Infinitely Many Ferries Holding Infinitely Many Buses Carrying Infinitely Many Passengers? 17:00 Infinity Conundrum with Ping Pong Balls, A Vase, and a Barrel 17:40 What Is a Supertask? 20:00 Common Answers to the Ross Littlewood Paradox 22:30 What If You Want Just the Even Balls in the Vase? 23:20 Writing Out the Answers for the Infinity Conundrum in Mathematical Notation 24:30 A Lesson About Infinity 25:00 Avoid Paradoxes About Infinity 25:25 What Are Supertasks? 26:00 E. Brian Davies Theory on an Infinitely Powerful Computer 27:00 MakerBot Makes Another Makerbot 27:45 Why Does .9 Repeating Equal 1? ------------------------------------------- The Great Courses is the global leader in lifelong learning and our video-on-demand service The Great Courses Plus gives you unlimited, uninterrupted access to a world of learning anytime and anywhere you want it. With courses on thousands of topics, you are sure to find something that will ignite your curiosity and invigorate your passion for learning. Enjoy a curated sampling of our full catalog of content by subscribing to our YouTube channel. We add new history, science, and math videos every week. ------------------------------------------- Read articles from the smartest experts in their fields: www.Thegreatcoursesdaily.com Find us on all our social channels: -Facebook: www.facebook.com/wondrium -Twitter: twitter.com/wondrium -Instagram: www.instagram.com/wondrium ------------------------------------------- #infinity #paradoxes #mindbendingmath

Be the first to comment