The Banach–Tarski Paradox

The Banach–Tarski Paradox

Q: “What’s an anagram of Banach-Tarski?”
A: “Banach-Tarski Banach-Tarski.”


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infinity paradoxes:

Vi Hart on types of infinity:
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Banach-Tarski on wikipedia:

Banach-Tarski proofs:

Banach-Tarski explinations online:

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Hilbert’s hotel on wikipedia:

types of infinity:

set theory and quantum physics:

LHC gif:

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This Post Has 49 Comments
  1. You went wrong as soon as you started saying you can apply to a physical object because a material object exists within our own Universe where there is a minimal length and there is a smallest thing. Good luck continuing your mental masturbation beyond the Planck length

  2. Is it just me or is 1:48 faked? Look at the way the dollar is ripped there’s no way you can rip one dollar into those shapes because the rips would overlap resulting in even smaller pieces. I may be wrong I’m just pointing something out

  3. 6:00 Wrong, eventually the real numbers will be something like ….8888888…. and than your gonna have ….9999999…. and back to ….88888888….

  4. Trying to understand a concept that contradicts its own existence(which i consider as perfect,i.e., things that contradict themselves are PERFECT) would always result in things that don't make sense
    because it is never meant to be. Like what i am saying right now is absolutely wrong and so is every other sentence in this world ever said because every one of those and mine contain a definite amount of inconceivable uncertainty that we, humans, are unable to look through due to the fact of definiteness of our existence , that is precisely why we consider infinite as infinite otherwise we would have been relatively absolute to it and wouldn't consider it what we do now and it would have been some finite for us. (Just my casual reasoning)

  5. This ignores the law of phasing. If you transition from violet light to ultra violet light. At what point can you no longer see it? There will be a point at which you can no longer acknowledge it's existence. It stops existing to you.

    Just like how there are an infinite number of non-whole numbers between whole numbers, you can still count from 1 to 2. When you go from position A to position B how many positions in-between A and B is there? There are infinite positions in-between, but yet you can always walk from point A to point B and even past point B to point C. But this would mean you had to have exceeded infinity times infinity positions between to have ever reached point B or beyond.

    This is only possible because there is a point of division that the space between does not exist to us.

  6. Sure…lets just move our hands out of the frame for a split second while I act like I just laid these pieces of a dollar bill down right in front of me…never mind they've been sitting there the entire time. 😑

  7. Up, Up, Right, Right, Down, Down… all I could think about was my SNES and a spiral notebook.
    Those darn "spooky action" cheat codes…

  8. Poor people 😂😂 y the fuck you are using your brain so much .. zero is infinity in your view but zero is just a bridge to add another dimension ..infinity is necessary for correcting answer math needs to be accurate so fucking zero was invented.. other wise how could fit large numbr

  9. How close can two objects get to each other without touching?

    Isn't it mathematically impossible to touch anything?

    Example: u have 2 base balls and there 1 millimeter let's say you move it 0.00000000000 so on and so forth until uncountable infinity wouldn't be impossible to touch?

    Sry if my explanation is confusing

  10. in the hyperwebster section, you said "after an infinite numbers of a, we get to ab and then aba, abaa, …" but the point is the number of "a"s in aaaaaa… will never end, so we will never be able to get to ab, so the dictionary will be a huge infinite book filled with never ending "a"s.

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