# Suppose that Hilbert’s Grand Hotel is fully occupied on

## Problem 7E Chapter 2.5

Discrete Mathematics and Its Applications | 7th Edition

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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.

Step-by-Step 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.

Step 2:

The definition  of Hilbert’s Grand Hotel:

Hilbert’s Hotel is an Experiment which illustrates a counterintuitive property of infinite sets. therefore It is accomplished that a fully occupied hotel with infinitely many rooms may still accommodate additional guest and that this process may be repeated.

Step 3 of 4

Step 4 of 4

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