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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
   • Your Brain as Math  Part 1 | Infinit...  

Simplicial Complexes Your Brain as Math Part 2
   • Simplicial Complexes  Your Brain as ...  

Your Mind Is EightDimensional Your Brain as Math Part 3
   • Your Mind Is EightDimensional  Your...  

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 HoustonEdwards
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/...
https://plato.stanford.edu/entries/ax...
http://www.math.kth.se/matstat/gru/go...

Vsauce
   • The Banach–Tarski Paradox  

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!