Whatever the opinions of Banach or Tarski may have been on the validity of the AoC, we can relatively sure they did not develop the Banach-Tarski construction I describe in the article to comment on the AoC, because there was already a very weird AoC-based construction which had been well-known for 19 years prior to Banach and Tarski's publication of their result. The BTP may be used today to illustrate the consequences of the AoC more easily to a layman, but the original purpose of the construction was more involved with group orbits and (perhaps?) representation theory. I hope nobody minds if I make this minor change. [[User:JacobB|JacobB]] 21:44, 5 January 2010 (EST) | Whatever the opinions of Banach or Tarski may have been on the validity of the AoC, we can relatively sure they did not develop the Banach-Tarski construction I describe in the article to comment on the AoC, because there was already a very weird AoC-based construction which had been well-known for 19 years prior to Banach and Tarski's publication of their result. The BTP may be used today to illustrate the consequences of the AoC more easily to a layman, but the original purpose of the construction was more involved with group orbits and (perhaps?) representation theory. I hope nobody minds if I make this minor change. [[User:JacobB|JacobB]] 21:44, 5 January 2010 (EST) |