The Grand Hotel Cigar Mystery
Another story regarding the Grand Hotel can be used to show that mathematical induction only works from an induction basis.
Suppose that the Grand Hotel does not allow smoking, and no cigars may be taken into the Hotel. Despite this, the guest in room 1 goes to the guest in room 2 to get a cigar. The guest in room 2 goes to room 3 to get two cigars—one for himself and one for the guest in room 1. In general, the guest in room N goes to room (N+1) to get N cigars. They each return, smoke one cigar and give the rest to the guest from room (N-1). Thus despite the fact no cigars have been brought into the hotel, each guest can smoke a cigar inside the property.
The fallacy of this story derives from the fact that there is no inductive point (base-case) from which the induction can derive. Although it is shown that if the guest from room N has N cigars then both he and all guests in lower-numbered rooms can smoke, it is never proved that any of the guests actually have cigars therefore it doesn't follow that any guest can smoke a cigar inside the Hotel. The fact that the story mentions that cigars are not allowed into the hotel is designed to highlight the fallacy. However, since there is an infinite number of rooms in the hotel and each guest (N) must go to guest (N+1) for his cigar, this process of going up one room never ends and no cigars are ever smoked.
Read more about this topic: Hilbert's Paradox Of The Grand Hotel
Famous quotes containing the words grand, hotel, cigar and/or mystery:
“Writing a book of poetry is like dropping a rose petal down the Grand Canyon and waiting for the echo.”
—Don Marquis (1878–1937)
“I’ve always thought a hotel ought to offer optional small animals.... I mean a cat to sleep on your bed at night, or a dog of some kind to act pleased when you come in. You ever notice how a hotel room feels so lifeless?”
—Anne Tyler (b. 1941)
“The slogan ‘45 minutes in Havana’ was not coined in the Cuban city, but in a Yankee cigar factory here.”
—Administration for the State of Con, U.S. public relief program (1935-1943)
“What constitutes a real, live human being is more of a mystery than ever these days, and men—each one of whom is a valuable, unique experiment on the part of nature—are shot down wholesale.”
—Hermann Hesse (1877–1962)