What happens if you just keep squaring?

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There's a strange number system, featured in the work of a dozen Fields Medalists, that helps solve problems that are intractable with real numbers. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription. If you're looking for a molecular modeling kit, try Snatoms - a kit I invented where the atoms snap together magnetically: https://snatoms.com ▀▀▀ References: Koblitz, N. (2012). p-adic Numbers, p-adic Analysis, and Zeta-Functions (Vol. 58). Springer Science & Business Media. Amazing intro to p-adic numbers here: https://youtu.be/3gyHKCDq1YA Excellent series on p-adic numbers: https://youtu.be/VTtBDSWR1Ac Great videos by James Tanton: @JamesTantonMath ▀▀▀ Special thanks to our Patreon supporters: Emil Abu Milad, Tj Steyn, meg noah, Bernard McGee, KeyWestr, Amadeo Bee, TTST, Balkrishna Heroor, John H. Austin, Jr., john kiehl, Anton Ragin, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Juan Benet, Ubiquity Ventures, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Sam Lutfi. ▀▀▀ Written by Derek Muller and Alex Kontorovich Edited by Trenton Oliver Animated by Mike Radjabov, Ivy Tello, Fabio Albertelli and Jakub Misiek Filmed by Derek Muller Additional video/photos supplied by Getty Images & Pond5 Music from Epidemic Sound & Jonny Hyman Produced by Derek Muller, Petr Lebedev, & Emily Zhang