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Elementary Lessons in Logic; Deductive and Inductive, . with Copious Questions and Examples, and Vocabulary of Logical Terms

Elementary Lessons in Logic; Deductive and Inductive, . with Copious Questions and Examples, and Vocabulary of Logical Terms


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About the Book

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...but not the same tie of similarity. It was at one time believed that if any integral number were multipled by itself, added to itself and then added to 41, the result would be a prime number, that is a number which could not be divided by any other integral number except unity; in symbols, x' + x+l =prime number. This was believed solely on the ground of trial and experience, and it certainly holds for a great many values of x. Thus when x is successively made equal to the numbers in the first line below, the expression x+x + $i gives the values in the second line, and they are all prime numbers: 0123456789 10 41 43 47 53 61 71 83 97 113 131 151 No reason however could be given why it should always be true, and accordingly it is found that the rule does not always hold true, but fails when x=&p. Then we have 40x40-1-40 + 41 = 1681, but this is clearly equal to 41 x 40 + 41 or 41 X41, and is not a prime number. In that branch of mathematics which treats of the peculiar properties and kinds of numbers, other propositions depending solely upon observation have been asserted to be always true. Thus Fermat believed that 22 +1 always represents a prime number, but could not give any reason for the assertion. It holds true in fact until the product reaches the large number 4294967297, which was found to be divisible by 641, so that the generality of the statement was disproved. We find then that in some cases a single instance proves a general and certain rule, while in others a very great number of instances are insufficient to give any certainty at all; all depends upon the perception we have of similarity or identity between one case and another. We can perceive no similarity between all prime numbers which assures us that because one is represented by a ce...


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Product Details
  • ISBN-13: 9781231133798
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 124
  • Spine Width: 7 mm
  • Width: 189 mm
  • ISBN-10: 1231133791
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 236 gr


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