Counting To Infinity And Beyond On A Chessboard
- 6 years ago
The numbers infinity plus 1 and infinity squared sound like they are made up, but mathematicians do use such numbers in set theory. They are called transfinite ordinals and they arise in combinatorial game theory. This video demonstrates an example of a transfinite value from a special game of chess.\r
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Correction: In the first example at 1:12 I said and wrote Ne6+. It should be Ne7+.\r
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My blog post summarizing this video: \r
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Paper referenced in video. C.D.A. Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, new. \r
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Francis Su lecture on transfinite ordinals\r
\r
\r
Joel David Hamkins lecture on infinite game theory\r
\r
\r
Special thanks to Patreons for supporting me and making this channel possible.\r
\r
Kyle\r
Alberto Nishikawa\r
Brian Mooney\r
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If you like my videos, you can support me at Patreon: \r
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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.\r
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My Books\r
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The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) \r
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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 5/5 stars on 1 review) \r
\r
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 4.5/5 stars on 11 reviews. \r
\r
Math Puzzles Volume 2 is a sequel book with more great problems. \r
\r
Math Puzzles Volume 3 is the third in the . \r
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40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) \r
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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 3 reviews) \r
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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 1 review)
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Correction: In the first example at 1:12 I said and wrote Ne6+. It should be Ne7+.\r
\r
My blog post summarizing this video: \r
\r
Paper referenced in video. C.D.A. Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, new. \r
\r
Francis Su lecture on transfinite ordinals\r
\r
\r
Joel David Hamkins lecture on infinite game theory\r
\r
\r
Special thanks to Patreons for supporting me and making this channel possible.\r
\r
Kyle\r
Alberto Nishikawa\r
Brian Mooney\r
\r
If you like my videos, you can support me at Patreon: \r
\r
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.\r
\r
My Blog: \r
Twitter: \r
Facebook: \r
Google+: \r
Pinterest: \r
Tumblr: \r
Instagram: \r
Patreon: \r
\r
Newsletter (sent about 2 times a year): \r
\r
My Books\r
\r
The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) \r
\r
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 5/5 stars on 1 review) \r
\r
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 4.5/5 stars on 11 reviews. \r
\r
Math Puzzles Volume 2 is a sequel book with more great problems. \r
\r
Math Puzzles Volume 3 is the third in the . \r
\r
40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) \r
\r
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 3 reviews) \r
\r
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 1 review)