Re: Proposal: 6NF

"David Cressey" <dcressey_at_verizon.net> wrote in message news:8VWWg.1111$P92.756_at_trndny02...
>
> "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.
>

Hi David

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.

--Brian Received on Wed Oct 11 2006 - 04:13:27 CEST