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by lanstin
633 days ago
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For example, the Banach-Tarski paradox can't happen in two dimensions, it needs at least three. Terence Tao's 2nd book on analysis explains it, tho I can't yet understand the explanation. (It (the weird measure expanding rearrangement) can happen for countable # of sets in 2, even 1 dimension, but not for finite # of sets). https://terrytao.files.wordpress.com/2010/02/epsilon.pdf |
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