Math's Strangest Set

Video Description

The Vitali Set is a set that has no size. It’s not that it’s size is 0 or infinity, or that we just haven’t found the right tools to measure it. This set can’t possibly have any size whatsoever. _____ Join my Patreon community: https://www.patreon.com/abidebyreason Support the channel with a one-time donation: https://ko-fi.com/abidebyreason _____ Related Videos: What is a Banach Space? https://youtu.be/Zjo1ACFm5WI What is a Hilbert Space? https://youtu.be/FFPXm-tuOt8 The Lebesgue Integral: https://youtu.be/Fb2ei6lD-d8 _____ Corrections: 1. at around the 08:30 mark, I wrote "all rationals in [0,1] can be put into a list". This is true. However, in this video's context it should be "all rationals in [-1,1] can be put into a list". 2. at the 5:00 mark, several of the irrationals I pick out of the box are not in [0,1] (like pi, pi/4 +1/2, and sqrt(2)). They should all be in [0,1]. So instead they should be pi/7, pi/4 - 1/2, and sqrt(2)/4. _____ Music: Epidemic Sound Animations created using Manim: https://www.manim.community/