Changes

==Interpretation==

==Interpretation==

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 set]]s, 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 set]]s, even though these do not match solid objects in the real world.

==External Links==

==External Links==