How Infinity Explains the Finite | Infinite Series

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

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