Re: Stored fields ordered left to right

"Jonathan Leffler" <jleffler_at_earthlink.net> wrote in message news:tgqLb.1171$Pg.92_at_newsread1.news.pas.earthlink.net...
> Mike Preece wrote:
> > [...various non-illuminating diatribes omitted...]
> > If I'm following this discussion correctly, you're saying the word
> > "relational", in the generally accepted context of "relational
> > databases", has a different meaning when used in a strictly
> > mathematical context.
> >
> > The difference has something to do with "ordering". I don't
> > understand. Sorry.
> >
> > Is it important? and if so, why?
>
> Possibly the simplest thing to do is look at the original paper, which
> is available online at:
>
> http://www.acm.org/classics/nov95/toc.html
>

Yes, the info is in Codd's 1970 paper, but for those who do not prefer to read more mathematical jargon than necessary for this particular point, it is this:

A mathematical relation is a set of ordered tuples {a1, a2, ..., an} with certain characteristics.

A Codd's relation, however, removes the ordering by injecting a unique name plus the name of the set all of the information is there without ordering the elements. So relational database theorists think that relations MUST be unordered, when in fact it is they who opted not to use the mathematical definition of the term.

My point in stating this is that I'm writing up responses to a set of questions that Chris Date put out regarding the MultiValue model and claims that MultiValue must not be relational (and I'll admit it isn't by his definitions) because it has ordered tuples. That argument always just sounds out-n-out wrong to me since mathematical relations are ordered tuples, dag nab it! So, I just had to clear this little matter up. MultiValue uses mathematical relations which are, in fact, also functions (they map a unique key to an ordered tuple) but it does not use Codd's definition of a relation simply because there is an ordering on the tuples.

I wasn't trying to say "nah nah na boo boo, relational databases are not mathematical relations like MultiValue databases are" (I'll leave that for others), but was simply trying to get a sound, logical, and fair response for Mr. Date. Cheers! --dawn

> As I pointed out earlier in one of these threads (possibly even this
> one), there is a section in this about the difference between ordered
> mathematical relations and unordered 'relationships' used in RDBMS,
> and why that is important. My take on it is that the primary issue is
> usability - people have a harder time using numbers to identify
> columns than using names.
>
> --
> Jonathan Leffler #include <disclaimer.h>
> Email: jleffler_at_earthlink.net, jleffler_at_us.ibm.com
> Guardian of DBD::Informix v2003.04 -- http://dbi.perl.org/
Received on Fri Jan 09 2004 - 06:39:48 CET