Re: Proposal: 6NF

"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. Received on Wed Oct 11 2006 - 02:28:52 CEST