Hilbert Infinite Hotel Paradox

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INTRESTING FACTS IN MATH


This is details about all interesting facts I learn in Math. 

Hilbert infinite hotel paradox. 

Today I will discuss the Hilbert infinite hotel paradox. 


Imagine a hotel with infinite rooms. And now infinite guests are already in each room.

So now the problem is we have new infinite guests coming to check-in the hotel.

How do we solve the problem where new guests also have rooms to stay? 

Let's assume that all the rooms are similar in size and each guest is a single guest. 


Now , we can solve by , putting each guest in 2*n where n is the hotel room number. 


So lets say guest A is in room # 1, he will go to room #2, guest from room # 2 will go to 4,

guest from #3 will go to 6, so on and so forth.


Old guest room #

New guest room #

1

2

2

4

3

6

10

20

15

30

17

34

123

246



 So now even rooms are filled. 

So now the new guests can go to odd number rooms starting from 1, 3, and so on. 


 

There are many other popular solutions for the same problem. This is one of the methods I like. 




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