NetNews Usenet Archive 1992 #30/NN_1992_30.iso/spool/comp/theory/2724

Text File | 1992-12-17 | 1.8 KB | 35 lines

Newsgroups: comp.theory
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From: [e-mail] (Frank-Roland Boernke)
Subject: Re: Real Numbers vs. Rational Numbers?
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Organization: University of Passau, Germany
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Date: Thu, 17 Dec 1992 14:21:50 GMT
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|> How about this:
|> Maybe the model could conceivably represent the reals, but how would any
|> irrational number get into the machine in the first place?  There are
|> uncountably many irrationals, so a table look-up won't do.  You could
|> try to calculate them, but how do you calculate, say, pi, with only
|> Turing-machine-like operations?
|>
|> So, at first glance, it looks like this machine is equivalent to the RAM
|> model with rationals plus a finite number of irrationals you could have in
|> a table.  This is equivalent to a Turing machine.
|>
|> Anybody buy that?
How is it possible to work with irrationals in a table? Of course you cannot store
them digit by digit as there is an infinite number. But if you choose a finite
representation e.g. two letters P and I for the sequence 3.141592654... how can
you calculate say PI * PI?

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