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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Additional resources for Automated Theorem Proving: After 25 Years
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.