NetNews Usenet Archive 1992 #30/NN_1992_30.iso/spool/comp/theory/2711

Text File | 1992-12-16 | 1.7 KB | 37 lines

Newsgroups: comp.theory
Path: sparky!uunet!mcsun!Germany.EU.net!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: Real Numbers vs. Rational Numbers?
Message-ID: <[e-mail]>
Sender: [e-mail] (News-Operator)
Organization: University of Passau, Germany
Date: Wed, 16 Dec 1992 09:54:12 GMT
Lines: 26

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.

Of course, e.g. you can compute Pi up to as many digits as you want, but in every
step  of computation you only have an approximation - a rational number.

Therefore, a machine-model, that allows real numbers, must be more powerful
than another one that does not. My professor said, that isn`t a problem but
I don`t agree. Who is right?

If I am wrong, please let me know where the fault is.

Thanks in advance.


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Frank Boerncke                       ,,,   University of Passau - Germany
[e-mail]     (.~.)            phone: [phone]
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