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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!
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\/ 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: math.colgate.edu/~integers/og2...
Omega*2 by Noam. D. Elkies: mathoverflow.net/a/63841/514442
Omega^4 by C. D. A. Evans, Joel Hamkins, and Norman Lewis Perlmutter: math.colgate.edu/~integers/rg4...
Omega_1 Proof by Matthew Bolan: mathoverflow.net/questions/63...
Subscribe to his channel! / @matthewbolan8154
Some clips are from Joel Hamkins presentation, “The theory of infinite games, including infinite chess”, watch it here! • TMWYF: The theory of i...
See more presentations on The Infinite Games Workshop: / @infinitegamesworkshop...
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: • Detective Music For In...
Looking For Clues by David Robson: • Suspenseful Detective ...
Witness Testimony by David Robson: • Mysterious Detective B...
Viking by Aakash Gandhi: • Viking - Aakash Gandhi
Mario Bava Sleeps In a Little Later Than He Expected To by Chris Zabriskie: • Mario Bava Sleeps In a...
This is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/...
Source: chriszabriskie.com/vendaface/
Artist: chriszabriskie.com/
Anime Song 2 by Montage of Chips: • Anime Song 2
Music: True Detective by Soundridemusic
Link to Video: • Suspense Detective, Cr...
White Hats by Wayne Jones: • White Hats - Wayne Jones
Artemis by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: • 'Artemis' [Inspiration...
Needle In A Haystack by David Robson: • Investigation Crime Sc...
Signal to Noise by Scott Buckley - released under CC-BY 4.0. www.scottbuckley.com.au
Video: • 'Signal to Noise' [Cin...
Weirder Stuff by Geographer: • Weirder Stuff - Geogra...
Many of these songs are provided by FesliyanStudios! Make a donation to also gain access to their music :) www.fesliyanstudios.com/policy
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 Pixabay.com
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".