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the transfinite subway

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Station 0 is at the airport, and the Hilbert hotel is at station w_1 (the first uncountable cardinal). The subway starts its journey empty. Aleph_0 passengers board the subway to the Hilbert hotel at the airport (station 0), and off it goes. The puzzle: when the subway pulls up to the Hilbert hotel at station w_1, how many passengers are on it? Is it 0, aleph_1, some determinate value in between, or indeterminate? -- Scott Huddleston sc...@crl.labs.tek.com I hope this wasn't meant to be a philisophical question, or I will be flamed very badly. After station 0, there will always be an infinite number of people on the subway. Therefore, the one passenger disembarking makes no difference. Hence we will have added aleph_0 passengers aleph_1 times, and hence the total number of passengers on the subway at the end is aleph_1. Stephen Montgomery-Smith mathsms@umcvmb ste...@mont.cs.missouri.edu Is the train *ever* going to pull up at the Hilbert hotel??? (half :-) All the usual tricks for maki

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