In a message dated 3/12/01 11:44:39 AM EST, [log in to unmask] writes: > How do we know the computer had examined "every" case It is the job of the mathematicians is to determine what is mathematically meant by "every case". That's done all the time. For example, in poker, the "odds" of getting five cards of the same suit is determined by calculating the NUMBER of ways five randomly drawn cards can be of the same suit, and then dividing that number by the TOTAL NUMBER OF WAYS any five cards can be drawn from a 52 card deck. In the case of the map problem, the **mathamaticians** (such as Professor Appel), and NOT the computer, had determined what "every case" was. You can choose to believe this or not. You can conjecture, out of the clear blue sky, that they had forgotten a few cases. If you do choose to publicly state that they have forgotten a case or two, I hope you explain your reasons so the correctness of your arguments can be mathematically ascertained. If the number of cases had been infinite, the computer would be out of its league as a tool. But since the number of cases turned out to be finite, the computer was able to solve the problem by examining every case. > How do we know the computer had examined "every" case > when we know any computer is limited in the highest number > it can deal with? > > pat You are mixing apples and oranges. The English alphabet is limited to 26 letters. How many words can be invented? How many books can be written? The number of digits in the decimal system is limited to 10. How many numbers can be expressed? -- Steve --