How Infinity Explains the Finite | Infinite Series

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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.

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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

Видео How Infinity Explains the Finite | Infinite Series канала PBS Infinite Series