[2rs1]

Am I the only one that has a problem wrapping my head around the infinity times infinity argument?

If you got infinity people on infinity busses, you would only have infinity people, not infinity squared. The moment when you close down the first bus and start with person 1 on bus 2, this person should already be on bus 1, or else must bus 1 be finite.

[tokenadult]

The Wikipedia article

http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gran...

relates one method of numbering passengers on the buses to count them (which I found in another source,

http://faculty.cua.edu/glenn/187f09/hilbert_hotel.pdf

which I used to teach my elementary-age class last Saturday the same trick), which shows that countably infinite buses with countably infinite passengers in each bus can still be accommodated by Hilbert's Hotel, even if all rooms are occupied when the buses arrive.

[harpastum]

I think one aspect you're missing is that infinity does not always mean everything. For example, there are infinite decimals between 1.0 and 2.0, and between 3.0 and 4.0 — however, there is no overlap at all between the sets.

That's how I imagined the busses to be; two non-overlapping infinite sets. No one from the first bus was also on the second.

[pilif]

that was IMHO the point of the first part of the article. You would never be able to close down the first bus because it does contain an infinite amount of people, so you need to find a way to process people across buses if you want to process the all.