Suppose that Hilbert’s Grand Hotel is fully occupied on

Chapter 2, Problem 7E

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QUESTION:

Problem 7E

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.

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QUESTION:

Problem 7E

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.

ANSWER:

Solution:

Step 1:

We need to show that the current guests can be spread out to fill every room of the two buildings of the hotel.

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