alxx100
Re:Bertrand Russell’s infinite sock drawer
on Saturday June 13, 2020 @05:53AM (#23508271)
It has little to do with the Hilbert Hotel. It is sufficient to decompose the original ball into 5 (!) pieces:
https://mathworld.wolfram.com/Banach-TarskiParadox.html
It is an existence proof that relies on the Axiom of Choice, of course there is no algorithm to actually construct those pieces.
This is one of the reasons that people distinguish between ZFC and ZF (Zermelo-Fraenkel with and without AC).
ZFC is not regarded as sound by some because of these Paradoxes.