Re: Real Numbers vs. Rational Numbers?

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Article #1880

#1880

From: Andrew Butterfield
Date: Tue, 05 Jan 1993 14:08

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In article <4287@dozo.and.nl>, jos@and.nl (Jos Horsmeier) wrote:
> 
> In article <1993Jan3.151347.29159@tom.rz.uni-passau.de> boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke) writes:
> 
> |For 2/5 you can find a finite numeric representation ( 0.4 )
> |for PI or PI*PI you cannot!
> 
> But what if we use a base PI representation? PI*PI obviously equals 100,
> which is definitely a finite numeric representation. There is none for 2/5,
> when using base PI.
> 
> kind regards and happy new year!
> 
> Jos aka jos@and.nl

You cannot represent 1, 2, 3, exactly either --- "base PI" doesn't seem
much use.

Say we have 12 and 23 as numbers in your base PI, how do we add them ?
What gets carried and how is it represented ?

The key point is that no matter what base you choose, it will not be
capable of 
giving a finite representation to all real numbers. Real numbers are
inherently
infinite objects.

Andrew Butterfield,                        butrfeld@cs.tcd.ie
Dept. of Computer Science, Trinity College, Dublin 2, IRELAND

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Path: arc1-ca.pugleaf.net!sparky!uunet!mcsun!ieunet!tcdcs!butrfeld.cs.tcd.ie!user
From: butrfeld@cs.tcd.ie (Andrew Butterfield)
Subject: Re: Real Numbers vs. Rational Numbers?
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