How the Axiom of Choice Gives Sizeless Sets | Infinite Series

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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.

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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!