How Infinity Explains the Finite | Infinite Series

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    • Kill the Mathematical Hydra | Infinite Series   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... 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/Goodstei... The Hydra Game http://math.andrej.com/2008/02/02/the... The Hydra Game https://markhkim.com/blog/mathematics... Commenters who took on the additional Hydra challenges! Anirudh sreekumar    • Kill the Mathematical Hydra | Infinite Series   Arjun Ariyil    • Kill the Mathematical Hydra | Infinite Series   Dliess Mgg    • Kill the Mathematical Hydra | Infinite Series   JedBrunozzi    • Kill the Mathematical Hydra | Infinite Series   Karan Kumar    • Kill the Mathematical Hydra | Infinite Series   Nishada Banana    • Kill the Mathematical Hydra | Infinite Series   Vedant Bhutra    • Kill the Mathematical Hydra | Infinite Series