4 ms·
I'd really like someone to explain Banach-Tarski to me in some way that I can sort of understand. I understand it has to do with AOC, which seems totally reason
by neilk 19y ago
I'd really like someone to explain Banach-Tarski to me in some way that I can sort of understand. I understand it has to do with AOC, which seems totally reasonable, and then I'm lost.
Also, I have trouble with "incrementally" understanding this. I can understand that the limit of 1/n (n->INF) is 0, because even with large finite numbers we're getting close to 0, but no matter how many times I cut up an orange I detect no Banach-Tarski strangeness.
- tel 19y agoI honestly have a difficult time understanding the AC paradoxes, too. I recognize that it's totally necessary for many things (i.e. multidimensional integrals) and when it's consistent with a logical conclusion I have little trouble "seeing" it. Otherwise, though, not so much. I think it's interesting to see the connection between the AC and the Law of Excluded Middle which also causes paradoxical issues from time to time. http://en.wikipedia.org/wiki/Axiom_of_choice#Law_of_the_excluded_middle http://en.wikipedia.org/wiki/Axiom_of_choice#Law_of_the_excl...