Re: Possreps and numeric types

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Tue, 27 Mar 2007 11:32:49 GMT
Message-ID: <Bh7Oh.15888$PV3.164348_at_ursa-nb00s0.nbnet.nb.ca>

David Cressey wrote:
> "Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message
> news:Y6XNh.15604$PV3.159796_at_ursa-nb00s0.nbnet.nb.ca...
>

>>Marshall wrote:
>>
>>
>>>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.
>>
>>I don't think I would call resource exhaustion an acceptable limitation
>>when adding two numbers both approximately equal to 1.

>
> Just as a humorous digression, the Calculator utility released with windows
> 3.1 had a bug in the way it handled approximations. If you started with
> zero, subtracted 0.1, then added 0.1 you would get an answer slightly
> different from zero. I may be wrong about the value "0.1" but it was some
> relatively pedestrian decimal fraction, that might easily occur in
> practice. There was a patch release later that fixed this.

I remember playing with that bug years ago now that you mention it. Received on Tue Mar 27 2007 - 13:32:49 CEST