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Re: Puzzle in the history of maths
Posted:
Feb 21, 2013 11:13 AM


pepstein5@gmail.com wrote: > > I think I remember reading that it was difficult for the early pioneers of set theory such as Cantor to prove or accept that R has the same cardinality has R ^ 2. I don't understand why this was difficult for them to prove. Surely, if you provide many bright undergrads with only the knowledge that existed at the time, it's not a particularly difficult exercise. I've heard it said that it seemed counterintuitive that set A can have a greater geometric dimension than set B but still have the same cardinality. But I don't understand why that is counterintuitive.
One cannot turn the clock back.
 When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting



