🚀 go-pugleaf

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.
The terminology "REAL number", I believe, is not a formal
one, but one borrowed from something like FORTRAN where
they are simply meant to represent floating point
numbers.

Any rational number can be represented by the division
of 2 integers and are therefore easily handled by a
RAM or Turing machine.