How Infinity Explains the Finite

How Infinity Explains the Finite | Infinite Series

2017-02-02

[public] 175K views, 4.64K likes, 65.0 dislikes audio only

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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

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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

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