Suppose that Hilbert’s Grand Hotel is fully occupied on the day the hotel expands to a second building which also contains a countably infinite number of rooms. Show that the current guests can be spread out to fill every room of the two buildings of the hotel.
Suppose that Hilbert’s Grand Hotel is fully occupied on the day the hotel expands to a second building which also contains a countably infinite number of rooms. Show that the current guests can be spread out to fill every room of the two buildings of the hotel.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Suppose that Hilbert’s Grand Hotel is fully occupied on the day the hotel expands to a second
building which also contains a countably infinite number of rooms. Show that the current
guests can be spread out to fill every room of the two buildings of the hotel.
Expert Solution
Step 1
We know,
Hilbert's Grand Hotel is a thought experiment which gives counterintuitive property of infinite sets.
It also demonstrated that a fully occupied hotel with infinitely rooms may still accommodate additional guests, even infinitely many of them.
This process can be repeat infinite times.
This idea was first introduce by David Hilbert in 1924.
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