0.999... Repeating Is Equal To 1, But Something Like It Is Not (Introduction To The Surreal Numbers) скачать в хорошем качестве

0.999... Repeating Is Equal To 1, But Something Like It Is Not (Introduction To The Surreal Numbers)

Some of the comments appear to be based solely on reading the title or the thumbnail--so I've changed the title to more accurately reflect the contents. The surreal numbers contain the real numbers, and 0.9 repeating is equal to 1 in both. However, we think about 0.9 repeating conceptually as some number that is infinitely smaller than 1. There is such a number in the surreal numbers, and it is not equal to 1! 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/questio... http://forums.xkcd.com/viewtopic.php?... http://en.wikipedia.org/wiki/0.999...... 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_Numbe... I welcome thoughtful comments about the surreal numbers. If you like my videos, you can support me at Patreon:   / 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: https://mindyourdecisions.com/blog/ Twitter:   / preshtalwalkar   Facebook:   / 168446714965   Google+: https://plus.google.com/1083366085665... Pinterest:   / preshtalwalkar   Tumblr:   / preshtalwalkar   Instagram:   / preshtalwalkar   Patreon:   / mindyourdecisions   Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 32 reviews) http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews) http://amzn.to/1o3FaAg "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 4.4/5 stars on 13 reviews. http://amzn.to/1GhUUSH "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews) http://amzn.to/1NKbyCs "Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 5 reviews) http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 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 (rated 4.7/5 stars on 4 reviews) 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. (rated 5/5 stars on 3 reviews) http://amzn.to/XRm7M4