🚀 go-pugleaf

In article <1993Jan5.161955.11237@tom.rz.uni-passau.de>,
boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke) wrote:
> 
> 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.
> 
When you say "handles real numbers", do you mean that it can write real
numbers
into a single box on the tape ? If this is the case then your "R-Turing"
machine is different to a classic one, which has a potentially infinite
tape,
but only a finite set of symbols that it can write on the tape.

The R-Turing machine has an uncountably infinite set of symbols. It would
also need an uncountably infinite transition function to exploit the power
of its symbol set.

A classic Turing machine can "handle" real numbers in the same way as any
other computing devices, by working with finite approximations of those
real numbers.