Automated Theorem Proving: After 25 Years by W. W. Bledsoe, Donald W. Loveland

By W. W. Bledsoe, Donald W. Loveland

Publication annotation no longer to be had for this title.
Title: Automated Theorem Proving
Author: Bledsoe, W. W./ Loveland, Donald W. (EDT)
Publisher: Amer Mathematical Society
Publication Date: 1984/06/01
Number of Pages:
Binding kind: PAPERBACK
Library of Congress: 84009226

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In the final word DOCK there is also only one vowel , but in the second position. How does the vowel change position? There are three possibilities. It may hop from one location to the other; it may disappear altogether and reappear later on; or an extra vowel or vowels may be cre­ ated and subsequently eliminated. The third possibility leads pretty directly to the theorem. Since only one letter at a time change s , at some stage the word must change from having one vowel to having two. It can 't leap from having one vowel to having three, for exam- W H A T M A T H E M A T i C S is ABOUT pIe.

In current terminology, the whole numbers 0, 1, 2, 3, . . are known as the natural numbers. If negative whole numbers are included, we have the integers. Positive and negative frac­ tions are called rational numbers . Real numbers are more gen­ eral; complex numbers more general still. So here we have five number systems, each more inclusive than the previous : natural numbers , integers , rationals, real numbers , and com­ plex numbers . In this book, the important number systems will be the integers and the reals.

Mathematics helps us to do all these things , and often it is indispensable. For example, consider the spiral form of a snail shell. Ho w the snail makes its shell is largely a matter of chemistry and genetics. Without going into fine points , the snai l ' s genes include recipes for making particular chemicals and instruc­ tions for where they should go. Here mathematics lets us do the molecular bookkeeping that makes sense of the different chemical reactions that go on; it describes the atomic struc­ ture of the molecules used in shells , it describes the strength and rigidity of shell material as compared to the weakness and pliability of the snail's body, and so on.

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