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Banach-Tarski

Posted: Sat Nov 24, 2018 7:18 pm UTC
by Tamebeverage
So, having just watch the vsauce video on the Banach-Tarski paradox, I am clearly an expert /sarcasm.

Since I am very much not an accomplished mathematician, I am mostly asking to be told why my thoughts are wrong. The argument relies on using points whose final rotation is UDLR. It seems to me, though, that you may as well delete the last rotation, because with or without it the set remains the same. So then the set of rotations ending in U is the same as the set ending UDLR.

Again, I know I'm wrong, but I'm looking to be told -why-.

Re: Banach-Tarski

Posted: Tue Nov 27, 2018 5:44 am UTC
by Eebster the Great
UDLR is equal to no rotation at all, because up and down cancel and left and right cancel. But rotations in three dimensions are not commutative, so ULDR is not equal to UDLR. I don't know what part of the video you're referring to, so I can't really answer the question.