Re: Proposal: 6NF

David Cressey wrote:
> "Hugo Kornelis" <hugo_at_perFact.REMOVETHIS.info.INVALID> wrote in message
> news:96jdi251552m2rb54f8edjrmhitcld1kni_at_4ax.com...
> > On Fri, 06 Oct 2006 12:59:15 GMT, David Cressey wrote:
> >
> > >There is one point I'm confused on: what is the domain of the empty set?
> > >does it even have a domain? To me, the empty set of character strings
> is
> > >not "the same thing" as the empty set of integers. But I may be thinking
> > >like a computer person and not like a mathematician.
> >
> > Hi David,
> >
> > Here are some thoughts from someone who is far from a mathematician and
> > who is more a database practictioner than a database theorist, so take
> > them with whatever amount of salt you see fit.
> >
> > When I worked with sets during the Dutch equivalent of highschool, I
> > usually had to use a two-part notation. I can't replicate the symbols
> > here and I don't recall all the correct names, but it consisted of a
> > definition of a domain and a listing or formula to define the values. So
> > you could have a set that was defined as a subset of the domain of
> > positive integers consisting of the numbers 2, 4, and 7; but you could
> > also have a set defined as a subset of the domain of real values
> > consisting of the numbers 2, 4, and 7.
> > Later, after highschool, I started to see a simplified notation for sets
> > that exposes only the values in the set but not the domain.
> >
> > Are the two sets above equal? I guess that you could defend both answers
> > here - the sets have the same members, but not the same domain
> > definition. I also guess that the notation used can sometimes be an
> > indication of how the answer would be in any give UoD.
> >
> > For a general answer, I'm tempted to say that there have to be two
> > equality operators for set arithmetic, one looking at the values of the
> > set members only, the other also looking at the domain.
> >
> > Anyway, whatever you favor as an answer to the question of equality of
> > the two sets above - once you've chosen an answer, the answer to
> > equality of two empty sets logicallly follows.
> >
> > Best, Hugo
>
> Thanks for your reply, Hugo. I'm also more of a practitioner than a
> theoretician, and certainly no mathematician.
> So I'll take what you say with a grain of salt, and you can do the same with
> what I say.
>
> It's not clear to me that the real number 2 is the same thing as the integer
> 2. Just for clarity, let me represent the real number 2 as 2.0. It seems
> to me that {2.0, 4.0, 7.0} is not equal to {2, 4, 7} the elements are
> counterparts, but they aren't the same.

Surely the question of whether 2 and 2.0 are identical depends on the domains from which they arise. As discussed in an older thread, both 2 and 2.0 are just labels (or representations) given to some underlying item, and that item is defined by its domain (or type).

Consider that the int 2 and the unsigned-int 2 are different things for instance - if I deduct three from both, the latter becomes -1 but the former becomes 4,294,967,295 - a relatively significant difference :) Received on Wed Oct 11 2006 - 13:37:56 CEST