Re: Proposal: 6NF

"David Cressey" <dcressey_at_verizon.net> wrote in message news:4w5Xg.2135$lj2.1997_at_trndny01...
>
> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
> news:brYWg.13346$6S3.9621_at_newssvr25.news.prodigy.net...
>
>> The domain of integers is a proper subset of the domain of reals. I
>> think
>> the concept is called "specialization by constraint." That means that
> every
>> integer is also a real number; therefore, {2, 4, 7} is identical to {2.0,
>> 4.0, 7.0}. 2.0 and 2 are just possible representations of the same
> number,
>> which belongs not only to the set of all real numbers but also to the set
> of
>> all integers.
>
> Interesting. If you are right (and why wouldn't you be) then this is a
> place where my computer background is misleading me when I try to think
> mathematically. Floating point numbers and integers, in the computers of
> the 1960s, were not arranged in such a way that the binary representation
> of
> floating point 2.0 and the binary representation of integer 2 would be the
> same.

They still don't. It's not possible to represent every irrational number as a finite sequence of digits or bits, and there are an infinite number of irrational numbers. Those that have special significance, such as pi or e, could possibly be represented using special values, but the majority must still be represented as approximations.

> There were one or two such computers, but they were uneconomical in
> practical terms.
>

I would be interested to know how they did it.

> So when some early FORTRAN computer was asked to compute equals (2.0, 2)
> it would detect the type mismatch and convert one of the inputs so that
> they
> are of the same type. So the unconcious legacy in my head doesn't help
> in
> this case.
>
> I like the phrase "specialization by constraint". We periodically get
> would
> be database designers asking some variant of the gen-spec question.
> Usually, it's something along the line of wanting to represent "vehicles"
> and also specific types of vehicles such as "sedans", "SUVs", etc. The
> regulars in this newsgroup know what happens next. In any event, I'm
> wondering if the term "specialization by constraint" wouldn't be useful in
> helping newbies understand the gen-spec problem at the conceptual level,
> before understanding a table design that implements it.
>

Sounds like a good idea.

> Sorry for the digression.
>
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Received on Wed Oct 11 2006 - 16:33:12 CEST