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Currently Playing: How the Axiom of Choice Gives Sizeless Sets | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Does every set - or collection of numbers - have a size: a length or a width? In other words, is it possible for a set to be sizeless? This in an updated version of our September 8th video. We found an error in our previous video and corrected it within this version. Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episodes Your Brain as Math - Part 1 https://www.youtube.com/watch?v=M0M3srBoTkY Simplicial Complexes - Your Brain as Math Part 2 https://www.youtube.com/watch?v=rlI1KOo1gp4 Your Mind Is Eight-Dimensional - Your Brain as Math Part 3 https://www.youtube.com/watch?v=akgU8nRNIp0 In this episode, we look at creating sizeless sets which we call size the Lebesgue measure - it formalizes the notion of length in one dimension, area in two dimensions and volume in three dimensions. Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com) Resources: https://math.vanderbilt.edu/schectex/ccc/choice.html https://plato.stanford.edu/entries/axiom-choice/ http://www.math.kth.se/matstat/gru/godis/nonmeas.pdf Vsauce https://www.youtube.com/watch?v=s86-Z-CbaHA Special Thanks: Lian Smythe and James Barnes Thanks to Mauricio Pacheco and Nicholas Rose who are supporting us at the Lemma level on Patreon! And thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us at the Theorem Level on Patreon!