Banach-Tarski paradox love

Banach-Tarski paradox

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  • if assuming the Axiom of Choice, which states that any collection of sets, each containing at least one element, it is possible to make a selection of exactly one element from each set, the Banach-Tarski paradox says that states that a solid ball in 3-dimensional space can be split into a finite number of non-overlapping pieces, which can then be put back together in a different way to yield two identical copies of the original ball

    March 21, 2011