By Charles G. Moore
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Extra resources for An Introduction to continued fractions
Hank was in Philadelphia with me the night of February 14. Red: ( a) (b) (c) (d) I did not kill Laurel. I have never been in Trenton. I never saw Hank before now. Shorty lied when he said I am gUilty. Shorty: (a) (b) (c ) (d) Tony: (a) (b) (c) (d) I was in Mexico City when Laurel was murdered. I never killed anyone. Red is the guilty man. Joey and I are friends. Hank lied when he said he never owned a revolver. The murder was committed on St. Valentine's Day. Shorty was in Mexico City at that time.
If he was interested in this aspect and this aspect only, then he could have done with Figure lB, despite the fact that it is not the exact geometrical counterpart of the maze. A mathematical object that interests us only in the possible traversings that it represents is known as an abstract graph. (The word graph is more commonly used in mathematics to describe data that have been plotted. ) Figure 3 gives additional examples of graphs. FIGURE 3 This type of abstraction is really quite commonplace.
The program of systematizing them, however, has been vastly rewarding. Years of polishing the axioms have reduced them to a form that is of high simplicity. The rules I have just enumerated have been found to be necessary, and sufficient, to do the job of describing and operating the real-number system; throw anyone of them away and the system would not work. And, as I have said, the program of axiomatic inquiry has answered some fundamental questions about numbers and produced enormously fruitful new concepts.
An Introduction to continued fractions by Charles G. Moore