# Can you tell me this theory?

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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?

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There is no such theory, but the term you are looking for is "axiom of choice".

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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.

Thanks again.

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I think we reached a possible conclusion in this thread (scroll down to post #23), which apparently is based on the axiom of choice

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I've heard it being called the Orange and the Sun theory.

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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."

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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.

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Why do you say it's not a theorem?

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