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# How Infinity Explains the Finite
- URL: https://www.cascadepbs.org/show/infinite-series/episode/how-infinity-explains-the-finite-5quooy/
- Published: 2024-04-02T22:52:11.000Z
- Updated: 2025-08-21T06:37:47.000Z
- Description: Peano arithmetic proves many theories in mathematics but does have its limits.
- Author: Cascade PBS Staff
- Tags: Infinite Series, Season 1, Episode 11, #ZZZ_Episode_32ce52d0-4635-44d9-bf69-5160f00daee0, #episode, #ZZZ_Show_0efdefa6-fb6f-44e5-96f1-baf9a8c090e2, #geo-us, #v1.16

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.