NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/comp/theory/2741

Text File | 1992-12-21 | 1.9 KB | 41 lines

Newsgroups: comp.theory
Path: sparky!uunet!cs.utexas.edu!qt.cs.utexas.edu!yale.edu!ira.uka.de!math.fu-berlin.de!informatik.tu-muenchen.de!rz.uni-passau.de!kirk.fmi.uni-passau.de!boerncke
From: [e-mail] (Frank-Roland Boernke)
Subject: Re: Real Numbers vs. Rational Numbers?
Message-ID: <[e-mail]>
Sender: [e-mail] (News-Operator)
Organization: University of Passau, Germany
References: <[e-mail]> <[e-mail]>
Date: Mon, 21 Dec 1992 10:35:27 GMT
Lines: 29

In article <[e-mail]>, [e-mail] (Eric Taylor) writes:
|> In article <[e-mail]>, [e-mail] (Frank-Roland Boernke) writes:
|> |> In lectures we talked about the RAM, a formal machine-model that is proved
|> |> to be as powerful as turing-machines(TM) and vice versa, according to the
|> |> Church-Turing-Thesis. This seems to be ok until you say, that the RAM allows
|> |> only natural numbers in its registers (or rational-numbers, since they are
|> |> countable). Our professor told us, that RAMs are allowed to store REAL numbers
|> |> too AND they are  still as powerful as an ordinary turing machine. I claimed, this
|> |> can`t be true, since there isn`t any possibility to work with irrational
|> |> numbers in TMs.
|>
|> REAL numbers are always RATIONAL numbers and vice-versa.

I dont't agree.

|>
|> Any rational number can be represented by the division
|> of 2 integers ...

This is the point: There are REAL number (the irrational ones) that cannot
be represented by the division of 2 integers (e.g. PI or e).



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Frank Boerncke                       ,,,   University of Passau - Germany
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