PBS Infinite Series | How Infinity Explains the Finite | Infinite Series @pbsinfiniteseries | Uploaded 7 years ago | Updated 2 hours ago
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: 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
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
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
markhkim.com/blog/mathematics/killing-the-hydra
Commenters who took on the additional Hydra challenges!
Anirudh sreekumar
youtube.com/watch?v=uWwUpEY4c8o&lc=z13ls3jzexjnyhkqp04chzoibx2itfryjro0k
Arjun Ariyil
youtube.com/watch?v=uWwUpEY4c8o&lc=z12bttoouvibd3yac04chnmopq23dnr5yhc
Dliess Mgg
youtube.com/watch?v=uWwUpEY4c8o&lc=z12eytdz0xn5edk5o04cevyojsuyzxjysmk0k
JedBrunozzi
youtube.com/watch?v=uWwUpEY4c8o&lc=z12fgjeolp3ki1qfn23zsjqpexizvvuea
Karan Kumar
youtube.com/watch?v=uWwUpEY4c8o&lc=z12rexh50su5gtsbg04cgj1hcvzvf5uxtp00k
Nishada Banana
youtube.com/watch?v=uWwUpEY4c8o&lc=z12bel3qsoqze5i3y22kgp5zlovvwsfk
Vedant Bhutra
youtube.com/watch?v=uWwUpEY4c8o&lc=z12rjrugdpfbcbfrn04cdrehiovsex3wv04
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: 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
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
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
markhkim.com/blog/mathematics/killing-the-hydra
Commenters who took on the additional Hydra challenges!
Anirudh sreekumar
youtube.com/watch?v=uWwUpEY4c8o&lc=z13ls3jzexjnyhkqp04chzoibx2itfryjro0k
Arjun Ariyil
youtube.com/watch?v=uWwUpEY4c8o&lc=z12bttoouvibd3yac04chnmopq23dnr5yhc
Dliess Mgg
youtube.com/watch?v=uWwUpEY4c8o&lc=z12eytdz0xn5edk5o04cevyojsuyzxjysmk0k
JedBrunozzi
youtube.com/watch?v=uWwUpEY4c8o&lc=z12fgjeolp3ki1qfn23zsjqpexizvvuea
Karan Kumar
youtube.com/watch?v=uWwUpEY4c8o&lc=z12rexh50su5gtsbg04cgj1hcvzvf5uxtp00k
Nishada Banana
youtube.com/watch?v=uWwUpEY4c8o&lc=z12bel3qsoqze5i3y22kgp5zlovvwsfk
Vedant Bhutra
youtube.com/watch?v=uWwUpEY4c8o&lc=z12rjrugdpfbcbfrn04cdrehiovsex3wv04
