🚀 go-pugleaf

In article <7111@tivoli.UUCP>, taylor@foraker.NoSubdomain.NoDomain (Eric Taylor) writes:
|> In article <1992Dec16.095412.19570@tom.rz.uni-passau.de>, boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke) writes:
|> |> 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. 
|> 
|> REAL numbers are always RATIONAL numbers and vice-versa.

I dont't agree.

|> 
|> Any rational number can be represented by the division
|> of 2 integers ...

This is the point: There are REAL number (the irrational ones) that cannot
be represented by the division of 2 integers (e.g. PI or e).



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