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Originally posted by Stradlater: I'm not familiar with the banach-tarski paradox, strange (link please?)...but this reminds me of the simple proof in which 2=1, but the problem was that there was a divide-by-zero, I wonder if certain mathematical rules are broken in the example you mention, but perhaps not. |
No, in the aformentioned paradox, the "trick" lies in the usage of a certain step that has been used to "prove" many other mathematical ideas that most mathematicians hold to be "true". We have not yet been able to prove many of these ideas without that step, and people continue to use it as if it were "true". Banach and Tarski were trying to show the mathematic community just how ridiculous they were being by continuing to use this step in their proofs. However, it didn't stop them.
As far as linking the paradox, I haven't found the ideal link, so I'll just point you to Google. There are a ton of pages out there on the subject as it is a fairly popular paradox.