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Text File  |  1993-01-03  |  1.5 KB  |  42 lines
  1. Newsgroups: comp.theory
  2. Path: sparky!uunet!math.fu-berlin.de!informatik.tu-muenchen.de!rz.uni-passau.de!kirk.fmi.uni-passau.de!boerncke
  3. From: boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke)
  4. Subject: Re: Real Numbers vs. Rational Numbers?
  5. Message-ID: <1993Jan3.151347.29159@tom.rz.uni-passau.de>
  6. Sender: news@tom.rz.uni-passau.de (News-Operator)
  7. Organization: University of Passau, Germany
  8. References: <1992Dec16.095412.19570@tom.rz.uni-passau.de> <1992Dec16.222628.27208@ringer.cs.utsa.edu> <1992Dec17.142150.7932@tom.rz.uni-passau.de> <1hi8dvINN5l2@uwm.edu>
  9. Distribution: inet
  10. Date: Sun, 3 Jan 1993 15:13:47 GMT
  11. Lines: 29
  12.  
  13. [... deleted ...]
  14. |> 
  15. |> Calculate PI * PI.
  16. |> Answer: PI*PI.
  17. |> 
  18. |> Since "PI*PI" is a finite representation of PI * PI from which one can
  19. |> algorithmically computer any of its digits in finite time, this counts as a
  20. |> valid answer.
  21. |> 
  22. |> If you don't consider this valid, then neither will you consider this valid:
  23. |> 
  24. |> Calculate: 2 / 5
  25. |> Answer: 2/5.
  26. |> 
  27. |> So then on that account, computers can't even work with fractions.
  28.  
  29. I think there IS a difference:
  30.  
  31. For 2/5 you can find a finite numeric representation ( 0.4 )
  32. for PI or PI*PI you cannot!
  33.  
  34.  
  35.  
  36.  
  37. -------------------------------------------------------------------------
  38. Frank Boerncke                       ,,,   University of Passau - Germany
  39. boerncke@kirk.fmi.uni-passau.de     (.~.)            phone: +49 0851 2267
  40. --------------------------------oOO--(_)--OOo---------------------------
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