Surreal: 0.999... Repeating Is Not Equal To 1 (Introduction To The Surreal Numbers)

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• published: 17 Sep 2014
• views: 60491

This video is meant to be an introduction to surreal numbers. Before you skewer me about the claim in the title, please WATCH the video and read the technical points below. Technical Points The surreal numbers are a pretty complicated logical system. One point to make is that the surreal numbers contain the real numbers, and so 0.999.. = 1 since this is true for the real numbers. However, there is a psychology about 0.999... repeating as a number that is infinitesmally smaller than 1. The surreal number {0, 1/2, 3/4, 7/8, ... | 1} is infinitesmally smaller than 1 and would satisfy our psychological idea of 0.999.. repeating. I believe {0, 9/10, 99/100, 999/1000, ...| 1} would also represent the same surreal number; however, I have not been able to verify that so I did not include it in the video. When fact-checking this video, I came across a number of conflicting arguments that seemed valid. http://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 http://forums.xkcd.com/viewtopic.php?f=17&t;=76752 http://en.wikipedia.org/wiki/0.999...#Hackenbush I also did my best to work through John Conway's book that introduces surreal numbers called "On Numbers and Games." http://en.wikipedia.org/wiki/On_Numbers_and_Games I welcome thoughtful comments about the surreal numbers. If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter: http://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: http://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: http://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books Here's a listing of all my books http://goo.gl/BDlEkB Here's a more detailed description of each book... "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4.2/5 stars on 17 reviews) http://amzn.to/1uQvA20 "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.6/5 stars on 9 reviews. http://amzn.to/1GhUUSH "Math Puzzles Volume 2" is a sequel book with more great problems. http://amzn.to/1NKbyCs "Math Puzzles Volume 3" is the third in the series. http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) http://amzn.to/1LOCI4U "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. http://amzn.to/XRm7M4