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The Banach–Tarski Paradox

Vsauce · explainer · Watch on YouTube

Logic & formal methodsPure mathematicsRecreational & visual math

What it is

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.

Why Hacker News recommends it

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

  • 6 people recommended it
  • 7 different months
  • 1 strong recommendations
  • first 2015, last 2024

What HN commenters said

  1. “This vsauce video is actually a really accurate (and entertaining!) introduction to set theory”

    Accurate and entertaining introduction to set theory and ordinals

    Aicy, 2021-09 · Strong recommendation · in “Intermediate Algebra”

  2. “(mindblown)”

    Mind-blowing math video among a list of STEM channels

    espeed, 2017-02 · Recommendation · in “The Essence of Linear Algebra [video]”

  3. “Have a look at how vsauce explains Banach-Tarsky [1]”

    Shows how far visual explanation of Banach-Tarski can go

    shezi, 2020-07 · Recommendation · in “Sphere Eversion”

  4. “you may need to pause them and rewatch them a few times to understand the details.”

    Half-hour Banach-Tarski explainer worth rewatching

    gus_massa, 2022-04 · Recommendation · in “I stopped working on black hole information loss”

  5. “It's an infinite number of infinitely thin filaments from the center of the sphere going outward in every direction.”

    Visualizes the sphere as infinitely thin filaments

    josephcsible, 2023-01 · Recommendation · in “The Point of the Banach Tarski Theorem”

  6. “years ago I watched this video from Vsauce about this very topic, and IIRC it was explained quite nicely”

    Nice explanation of the Banach-Tarski paradox

    djvdq, 2024-06 · Recommendation · in “Banach–Tarski Paradox”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: infinity, set theory, paradox, vsauce, measure theory

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