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

MiketheViking90 commented on the word Banach-Tarski paradox

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