The Banach–Tarski Paradox

Vsauce · 49.1M views · 2015-08-01 · 24:14

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Overview

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

On Hacker News

Recommended as an accurate, entertaining on-ramp to set theory and infinity, worth pausing and rewatching.

Recommended by 6 HN people across 7 months · HN mentions 2015–2024

Topics

Logic & formal methods Pure mathematics Recreational & visual math

What people said

Aicy · 2021-09 · Strong recommendation
Learn set theory! Specifically ordinals (just one formal defintion of a number) This vsauce video is actually a really accurate (and entertaining!) introduction to set theory: [VIDEO]
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djvdq · 2024-06 · Recommendation
I don't know if this will explain your questions, but years ago I watched this video from Vsauce about this very topic, and IIRC it was explained quite nicely: [VIDEO]
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josephcsible · 2023-01 · Recommendation
[VIDEO] nicely visualizes it. It's an infinite number of infinitely thin filaments from the center of the sphere going outward in every direction.
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Sources

Video by Vsauce, played through YouTube.

HN Library · Source license

Data and selection notes

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