🚀 go-pugleaf

In article <butrfeld-050193140552@butrfeld.cs.tcd.ie>, butrfeld@cs.tcd.ie (Andrew Butterfield) writes:
|> 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.
|> 

So what does this mean in the end? When I introduced this subject, I asked,
whether a Turing Machine, that handles not only bits or naturals but also 
real numbers is more powerful, than a turing machine, that only works 
with natural numbers. 

My professor said, both types of Turing Machines are the same concerning
their power of computability. I claimed that can't be true, refering to
ideas  like the ones mentioned in the quotes at the beginning of this side.

Who is right?




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Frank Boerncke                       ,,,   University of Passau - Germany
boerncke@kirk.fmi.uni-passau.de     (.~.)            phone: +49 0851 2267
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