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Topic: Puzzle in the history of maths
Replies: 5   Last Post: Feb 24, 2013 6:17 PM

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Frederick Williams

Posts: 2,166
Registered: 10/4/10
Re: Puzzle in the history of maths
Posted: Feb 21, 2013 11:13 AM
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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



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