Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity? Learn through active problem-solving at Brilliant: https://brilliant.org/InfiniteSeries Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode: Unraveling DNA with Rational Tangles https://www.youtube.com/watch?v=JXGyXtNsu14 Earlier videos referenced around 1:00 are: Cantor's paradox: https://www.youtube.com/watch?v=TbeA1rhV0D0 What are Numbers Made of? https://www.youtube.com/watch?v=S4zfmcTC5bM Peano axioms: https://www.youtube.com/watch?v=3gBoP8jZ1Is Hiearchy of Infinities: https://www.youtube.com/watch?v=i7c2qz7sO0I Vsauce How to Count Past Infinity https://www.youtube.com/watch?v=SrU9YDoXE88 Brilliant infinity wiki: https://brilliant.org/wiki/infinity/ Brilliant Number Theory course (with Exploring Infinity chapter): https://brilliant.org/courses/basic-number-theory/ Set theory arose in part to get a grip on infinity. Early “naive” versions were beset by apparent paradoxes and were superseded by axiomatic versions that used formal rules to demarcate "legal" mathematical statements from gibberish. Written and Hosted by Gabe Perez-Giz (@fizziksgabe) Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com) Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon. Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level! And thanks to Mauricio Pacheco and Andrew Poelstra who is supporting us at the Lemma level!