Re: So let me get this right: (Was: NFNF vs 1NF ...)
From: paul c <toledobythesea_at_oohay.moc>
Date: Thu, 10 Feb 2005 18:58:45 GMT
Message-ID: <F9OOd.355005$8l.28078_at_pd7tw1no>
>
>
>
> "The term relation is used here in its accepted mathematical sense.
> Given sets S1, S2, ... Sn (not necessarily distinct), R is a relation
> on these n sets of it is a set of n-tuples each of which has its first
> element from S1, its second from S2, and so on. {FN1}"
>
> {FN1} "More concisely, R is a subset of the Cartesian product S1 x S2 x
> ... x Sn."
>
> Now, what is the "accepted mathematical sense." of a "relation"? Well,
> to be sound the "mathematical understanding" should be free of
> paradoxes, and contradictions. As soon as you start saying "the set of
> domains includes sets of sets" or the like, you leap headlong into a
> twisted maze of paradoxes.
Date: Thu, 10 Feb 2005 18:58:45 GMT
Message-ID: <F9OOd.355005$8l.28078_at_pd7tw1no>
DBMS_Plumber wrote:
> Alfredo Asks:
>
>
>>>"Where Codd said that relational valued attributes are not [OK]"
>
>
>>From [1]
>
> "The term relation is used here in its accepted mathematical sense.
> Given sets S1, S2, ... Sn (not necessarily distinct), R is a relation
> on these n sets of it is a set of n-tuples each of which has its first
> element from S1, its second from S2, and so on. {FN1}"
>
> {FN1} "More concisely, R is a subset of the Cartesian product S1 x S2 x
> ... x Sn."
>
> Now, what is the "accepted mathematical sense." of a "relation"? Well,
> to be sound the "mathematical understanding" should be free of
> paradoxes, and contradictions. As soon as you start saying "the set of
> domains includes sets of sets" or the like, you leap headlong into a
> twisted maze of paradoxes.
that's a new one on me, assuming we aren't talking about self-referencing sets (eg. Russell's paradox) which is easy to avoid (perhaps that was the motivation for separate DDL and DML?). i'd like to see an example of a paradox that isn't easily avoided.
> ...
> My challenge to you is to find one single, stinkin' thing anyone else
> has ever written about the relational model of which the Date / Darwen
> crowd approved.
...
in the area of FD's and normalization alone, there are Armstrong's Axioms and many, many papers by people such as Ron Fagin.
pc Received on Thu Feb 10 2005 - 19:58:45 CET