Pre4edgc Posted February 6, 2008 Share Posted February 6, 2008 I'm trying to figure out the name of the theorem in which one sphere is cut into infinitely small pieces, and when put back together, it has the possibility of creating two spheres of the same volume as the original sphere. Can you help me? Link to comment Share on other sites More sharing options...
timo Posted February 6, 2008 Share Posted February 6, 2008 There is no such theory, but the term you are looking for is "axiom of choice". Link to comment Share on other sites More sharing options...
Pre4edgc Posted February 6, 2008 Author Share Posted February 6, 2008 Thanks for the information. It wasn't exactly what I was looking for, but then again, I may be wrong with the explanation... It might not even me mathematically related, but I could swear there was some sort of theory, principle, or something related to that. I think it may have been a link to a site that explained it in an earlier thread somewhere, but I'm not entirely sure what... Perhaps it was about 2+2=5? I'll see if I can find it. But thanks again. [EDIT] Ok. I found it. It was the Banach-Tarski Paradox that I was thinking of. http://www.scienceforums.net/forum/showthread.php?t=15428&highlight=sum+of+parts+whole+greater Thanks again. Link to comment Share on other sites More sharing options...
swansont Posted February 6, 2008 Share Posted February 6, 2008 I think we reached a possible conclusion in this thread (scroll down to post #23), which apparently is based on the axiom of choice Link to comment Share on other sites More sharing options...
the tree Posted February 7, 2008 Share Posted February 7, 2008 I've heard it being called the Orange and the Sun theory. Link to comment Share on other sites More sharing options...
swansont Posted February 7, 2008 Share Posted February 7, 2008 I've heard it being called the Orange and the Sun theory. That's the example mentioned in "Surely You're Joking, Mr. Feynman!" It often went like this: They would explain to me, "You've got an orange, OK? Now you cut the orange into a finite number of pieces, put it back together, and it's as big as the sun. True or false?" "No holes?" "No holes." "Impossible! There ain't no such a thing." "Ha! We got him! Everybody gather around! It's So-and-so's theorem of immeasurable measure!" Just when they think they've got me, I remind them, "But you said an orange! You can't cut the orange peel any thinner than the atoms." "But we have the condition of continuity: We can keep on cutting!" "No, you said an orange, so I assumed that you meant a real orange." Link to comment Share on other sites More sharing options...
alext87 Posted February 8, 2008 Share Posted February 8, 2008 To clear up the confusion. It is not actually a theorem by it is called the Banach–Tarski paradox. And it is a consequence of accepting the axiom of choice. Link to comment Share on other sites More sharing options...
the tree Posted February 8, 2008 Share Posted February 8, 2008 Why do you say it's not a theorem? Link to comment Share on other sites More sharing options...
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