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We explore extremely long Infinite Chess games, starting with Mate in Omega, and progressively climbing to higher and higher transfinite ordinals! Play Infinite Chess at: Support me and its development on my Patreon, and get your name in the credits of my videos: Join the Infinite Chess Discord server: Access the spreadsheet board editor: \/ Credits for the positions shown, along with links to learn more about them! \/ Omega, Omega^2, Omega^3 by Joel Hamkins and C. D. A. Evans: ~integers/og2/ Omega*2 by Noam. D. Elkies: Omega^4 by C. D. A. Evans, Joel Hamkins, and Norman Lewis Perlmutter: ~integers/rg4/ Omega_1 Proof by Matthew Bolan: #440147 Subscribe to his channel! Some clips are from Joel Hamkins presentation, “The theory of infinite games, including infinite chess”, watch it here! See more presentations on The Infinite Games Workshop: Note for the chapter “Climbing the Ordinal Tower”: I often mention “this to the power of this infinitely…”, or “infinite epsilons above this…”. When I word things like this, what I really mean is to take the limit, or supremum, as we approach doing that operation infinitely. I have chosen this wording to make things more intuitive to the viewer and those who may have zero ordinal arithmetic knowledge. This chapter is not meant to be a detailed explanation of ordinal arithmetic. 🎶 Music used (in order) 🎶 Background Check by David Robson: Looking For Clues by David Robson: Witness Testimony by David Robson: Viking by Aakash Gandhi: Mario Bava Sleeps In a Little Later Than He Expected To by Chris Zabriskie: This is licensed under a Creative Commons Attribution 4.0 license. Source: Artist: Anime Song 2 by Montage of Chips: Music: True Detective by Soundridemusic Link to Video: White Hats by Wayne Jones: Artemis by Scott Buckley - released under CC-BY 4.0. Video: Needle In A Haystack by David Robson: Signal to Noise by Scott Buckley - released under CC-BY 4.0. Video: Weirder Stuff by Geographer: Many of these songs are provided by FesliyanStudios! Make a donation to also gain access to their music :) Chapters: 0:00 Introduction 1:18 The Game Tree 3:21 Omega 5:17 Why Ordinals? 8:04 Omega 1 8:58 Omega*2 10:41 Omega^2 12:27 Omega^3 14:48 Omega^4 20:20 Matthew’s Proof 24:09 Climbing the Ordinal Tower 26:53 Conclusion Other stock footage is from If I missed, or incorrectly gave credit, please don’t hesitate to contact me using my email! Located in the “About“ section of my channel, click “View email address“.
