New PDF release: 3.1416 And All That

By Philip J. Davis, William G. Chinn (auth.)

ISBN-10: 0817633049

ISBN-13: 9780817633042

ISBN-10: 1461585198

ISBN-13: 9781461585190

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Sample text

This advance did not come readily. C. there appears to have been no systematic way of expressing large numbers. Archimedes then suggested a cumbersome method of naming them in his work The Sand Reckoner. Yet, while struggling with the names of large numbers, the Greek mathematicians took the jump from the finite to the infinite. The jump is signified by the three little dots after the 4 in the series above. They indicate that there is an integer after 4 and another after the successor to 4, and so on through an unlimited number of integers.

This leaves the job of screening out which of the two remaining statements is false. Sometimes two statements may necessarily have the same truth value such as Ra and Rd, or Hd and Jd; these are consistent statements. Sometimes two statements may necessarily have different truth values such as Rd and Sc; these are contradictory statements. We shall make use of these as we proceed. It will be helpful in following the discussion to keep track of what we have uncovered as we go along. This we can do in the form of a box score, as in Table 2.

It will be helpful in following the discussion to keep track of what we have uncovered as we go along. This we can do in the form of a box score, as in Table 2. SUSPECT HANK JOEY RED SHORTY TONY a b c t d t Table 2 We enter t or t in the box for the statement of each of these gentlemen according to whether the statement has been found to be true or false. So far, the only certainty we have are t's in Tony's box for band d. Next, look at Red's statements, a and d. Either Red is guilty or not guilty.

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3.1416 And All That by Philip J. Davis, William G. Chinn (auth.)


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