The story of Mr. Hilbert's hotel

I used to tell the story a little bit about the real variable function. from hAnsschwarzkopf

A long time ago, in a small town in a European country, Mr. Hilbert opened a hotel with countless rooms. One day, the hotel business was a mess, less than two o'clock in the afternoon, all the rooms are full of passengers. At this time, another visitor, asked to live in the hotel. The waiter told him that he was fully booked and was not receiving it. But the traveler still has to stay. This would have puzzled the experienced waiters. They had no choice but to invite the great Mr. Hilbert. Hilbert a little thought, and said to the waiter: "You let room 1th to move to room 2nd to go, Room 2nd passenger moved to room 3rd, and so on, and so, room 1th is not empty?" The waiter suddenly understood, so to sell the cake! In this way, the traveler was admitted to the hotel.

Who knows, the next morning, another 2013 passengers, the same request to stay at this hotel. You know, no one has checked out yet, and all the rooms are full of people. What do we do? The waiter finally learned from Mr. Hilbert that the passengers in room 1th moved to Room No. 2014, and room 2nd moved to Room No. 2015, so that 2013 rooms were vacated. In this way, the 2013 passengers also live in the hotel.

No matter what happened, trouble ensued. In the evening, no one has checked out, but yours faithfully guests are requested to stay at this hotel. At this time, the small waiter also for the great Mr. Hilbert learned a trick secretly proud, happy not to pass, who will think of the rainy days! What to do? The great Mr. Hilbert smiled and walked over.

"What's the matter with you, lad?" Mr. Hilbert asked.

"It is so, come to yours faithfully passengers, request to live in our hotel." "The staff was very helpful."

"What's so hard about that?" Let the passengers of room 1th move to room 2nd, the passenger of room 2nd moved to room 4th, and the passenger in room 3rd moved to room 6th, so the odd number room was not vacated? So that can be yours faithfully passengers can live under ". Mr. Hilbert was still smiling.

Marvelous In this way, the great Mr. Hilbert solved the problem.

The story of Mr. Hilbert's hotel