Re: Possreps and numeric types

On Mar 26, 2:39 am, "David Cressey" <cresse..._at_verizon.net> wrote:
> "Marshall" <marshall.spi..._at_gmail.com> wrote in message
>
> If the representation scheme for integers is indefinitely extensible, then
> the field of rationals representable is likewise indefinitely representable.
> Common decimal notation of integers is indefinitely extensible. There are
> other schemes.

Right.

> In any finite computer, it is only possible to actually represent a finite
> subset of the integers, and thus it is only possible to represent exactly a
> finite subset of the rationals. The problem is that the finite subset of
> rationals will not, in general, exhibit closure under addition. Thus one is
> forced into the realm of approximation as soon as one begins to store the
> results of arithmetic computation.

Well, again I object to the word "approximation." The result of a rational addition will either be an exact correct answer or a failure due to hitting a resource limitation. I would *not* call that an approximation.

Marshall Received on Mon Mar 26 2007 - 22:13:56 CEST