Some view the Banach-Tarski paradox as an absurd result, and evidence that the [[Axiom of Choice]] is false. This is the reaction of many non-mathematicians upon hearing this result. However, as one grows in mathematical understanding one finds it is impossible to avoid - mathematicians have learned to accept the existence of non-measurable sets, comfortable in the knowledge that they can never exist in the real world. | Some view the Banach-Tarski paradox as an absurd result, and evidence that the [[Axiom of Choice]] is false. This is the reaction of many non-mathematicians upon hearing this result. However, as one grows in mathematical understanding one finds it is impossible to avoid - mathematicians have learned to accept the existence of non-measurable sets, comfortable in the knowledge that they can never exist in the real world. |