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: 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: series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episodes Your Brain as Math - Part 1 Simplicial Complexes - Your Brain as Math Part 2 Your Mind Is Eight-Dimensional - Your Brain as Math Part 3 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 K