🚀 go-pugleaf

taylor@foraker.NoSubdomain.NoDomain (Eric Taylor) wrote:
> boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke) writes:
>> 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.

I think I'll have that one bronzed.  You'll be a *long*, *long* time living
that one down, pal.  Count yourself lucky that the trained ape who did your
news configuration has preserved you some measure of anonymity by obscuring
your site's identity.

Anyone else tempted to add their own bladderful to this torrent of
misinformation: there is a substantial literature on computing with real
numbers, ultimately going all the way to Brouwer's intuitionism of the
1920s, and you will look less of an idiot than these two if you read some
of it.  For starters you might get a copy of Lecture Notes in Computer
Science 613, "Constructivity in Computer Science", ed. J.P. Myers and M.J.
O'Donnell, Springer-Verlag 1991, and read back from the references in the
Chirimar/Howe, Tucker/Zucker, and Weihrauch papers there.

-- 
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