Suppose that Hilbert’s Grand Hotel is fully occupied, but

Chapter 2, Problem 6E

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QUESTION:

Problem 6E

Suppose that Hilbert’s Grand Hotel is fully occupied, but the hotel closes all the even numbered rooms for maintenance. Show that all guests can remain in the hotel.

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QUESTION:

Problem 6E

Suppose that Hilbert’s Grand Hotel is fully occupied, but the hotel closes all the even numbered rooms for maintenance. Show that all guests can remain in the hotel.

ANSWER:

Solution:

Step 1 :

In this problem in the Hilbert’s Grand Hotel is fully occupied, but the hotel closes all the even numbered rooms for maintenance then we have to prove that all guests can remain in the hotel.

Given in the problem by closing even numbered rooms,

Then we have the rooms number {1,3,5……}

All available room numbers are in the form of ,

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