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Curated by: PBS Infinite Series (69 videos)
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Peano arithmetic proves many theories in mathematics but does have its limits. In order to prove certain things you have to step beyond these axioms. Sometimes you need infinity. Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode - Kill the Mathematical Hydra https://www.youtube.com/watch?v=uWwUpEY4c8o Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com) Sources and further references: Kirby, L.; Paris, J. (1982). "Accessible Independence Results for Peano Arithmetic" (PDF). Bulletin of the London Mathematical Society. 14 (4): 285. doi:10.1112/blms/14.4.285 http://www.cs.tau.ac.il/~nachumd/term/Kirbyparis.pdf Goodstein, R. (1944), "On the restricted ordinal theorem", Journal of Symbolic Logic, 9: 33–41, doi:10.2307/2268019, JSTOR 2268019 https://www.jstor.org/stable/2268019 Goodstein Sequence http://mathworld.wolfram.com/GoodsteinSequence.html The Hydra Game http://math.andrej.com/2008/02/02/the-hydra-game/ The Hydra Game https://markhkim.com/blog/mathematics/killing-the-hydra/ Commenters who took on the additional Hydra challenges! Anirudh sreekumar https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z13ls3jzexjnyhkqp04chzoibx2itfryjro0k Arjun Ariyil https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z12bttoouvibd3yac04chnmopq23dnr5yhc Dliess Mgg https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z12eytdz0xn5edk5o04cevyojsuyzxjysmk0k JedBrunozzi https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z12fgjeolp3ki1qfn23zsjqpexizvvuea Karan Kumar https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z12rexh50su5gtsbg04cgj1hcvzvf5uxtp00k Nishada Banana https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z12bel3qsoqze5i3y22kgp5zlovvwsfk Vedant Bhutra https://www.youtube.com/watch?v=uWwUpEY4c8o&lc=z12rjrugdpfbcbfrn04cdrehiovsex3wv04
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