A Conversation for Infinity, and the Infinite Hotel Paradox
Cantor
Gnomon - time to move on Started conversation Oct 5, 2000
All this stuff about infinity is dealt with in Mathematics by the theory of countable and uncountable sets, developed by Georg Cantor. Hilbert knew this and developed the Hotel Paradox as a way of coming to grips with infinity and its peculiarities.
I think that no entry on the Hotel paradox would be complete without some of the mathematics that goes behind it.
The answer to the infinity of buses arriving, each with an infinite number of people on board, is yes, there is a way to make room for them all. One method is to get the people to form an orderly queue, taking the 1st person from 1st bus (1, 1), 2nd person from 1st bus (2,1), 1st person from 2nd bus (1,2), then (3,1), (2,2), (1,3), then (4,1), (3,2), (2,3), (1,4) and so on. The pattern here can be clearly seen if you draw it out on a chart. Now that the people are in line, you can send them into the hotel as before, with everyone in the hotel shifting up to twice their room number.
No doubt there are other ways.
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Cantor
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