Originally posted by chess kid1
Thx!
It ain't easy, kid. And why didn't you thank me for mine? :'( But just to prove that I'm not really upset, here's another one for your scrapbook:
There is a subway line from the airport to the Hilbert hotel which operates as follows: there is a station at each ordinal number, and every station is assigned a unique ordinal. The subway stops at each station, in order. At each station people disembark and board, in order, as follows:
i) if any passengers are on the subway, exactly 1 disembarks, then
ii) aleph_0 passengers board the subway.
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.
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?