On 15/07/2013 10:12, Warp wrote:
> scott <sco### [at] scottcom> wrote:
>> What happens if an infinite number of buses turn up at once?
>
> Wouldn't that be the power set of natural numbers, making it a genuinely
> larger set? Unless I have once again misunderstood something completely.

Thinking about it a bit more I came up with this:

People arriving on a bus, give them a bus number, B, from 1 to infinity, 
and a seat number, S, from 1 to infinity
People already in the hotel, give them bus number 0, and their seat 
number is their existing room number
Everyone then has a unique B and S number.

To map 2D integers to 1D you can use a formula like the cantor pairing 
function (had to look up what that was called, but I remember it from 
school) 0.5*(B+S)*(B+S+1)+S. This then gives you their new room number 
in the hotel.

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