The Banach-Tarski paradox

The Banach-Tarski paradox is a seemingly bizarre and outrageous claim that it is possible to take a ball, break it into a number of pieces and then reassemble those pieces to make two identical copies of the ball.

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[Kyanzes]

The Starsky-Hutch paradox is an advanced form of the original one.

[TheMemesofDestruction]

Love it! The algorithm recommended an old Vsauce Video about it recently and started exploring it. Thank you! ^.^

[YouWillNeverKnowMan]

My opinion is that the axiom of choice (which is super natural by itself) gets a bad rep only because it came after the others were already established and interacts in a weird way with the axiom of infinity (which, IMHO, is the real villain).

[jb]

I'm looking at Wikipedia, and it seems that the construction of subsets of the unit interval was done by Giuseppe Vitali, not by Hausdorff. But, Hausdorff was mentioned in the article as having done some other work on subsets of a sphere, so that could have been a more immediate predecessor to Banach-Tarski.

[Lemurinus]

A really good video. Enjoyed it very much.

[Nebulous_o]

Wondering if this paradox was given consideration (or inspiration!) to the mathematics that must surely have been applied to the molecular biology when successfully cloning dolly the sheep

[frankieboyseje]

what's the implications of this on a quantum particle level?