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Re: Stored fields ordered left to right

From: Dawn M. Wolthuis <dwolt_at_tincat-group.com>
Date: Fri, 26 Dec 2003 22:17:20 -0600
Message-ID: <bsj14k$hcs$1@news.netins.net>


"Joe "Nuke Me Xemu" Foster" <joe_at_bftsi0.UUCP> wrote in message news:1072496216.517226_at_news-1.nethere.net...
> "Dawn M. Wolthuis" <dwolt_at_tincat-group.com> wrote in message
<news:bsira5$jlt$1_at_news.netins.net>...
>
> > Marshall agreed with me on something, so I'll dare post one of the many
> > questions I have related to relational database theory.
> >
> > In Date's June 2003 paper entitled "What First Normal Form Really Means"
he
> > asks questions about MultiValue systems, which he (and no one else I've
> > read) abbreviates as "MVS". I am preparing answers to these questions.
> > Date writes "...MVS fields are ordered left to right (and so MVS files
are
> > certainly not relations, and the system is certainly not relational)."
> >
> > I've been puzzled by this for quite a while, just figuring that
relational
> > theorists have this wrong. But the writings seem so sure of this. I had
> > thought that the relations in relational database theory were
mathematical
> > relations, but I am beginning to think that might not be the case. My
> > masters in mathematics was quite some time ago, so I hauled out some
books
> > and googled a bit and everything I find that is mathematics, rather than
> > database theory, indicates what I thought about relations -- a relation
is a
> > set of ordered tuples -- right? What am I missing here? An element of
a
> > relation would be of the form (a1, a2, ... an) where a1 is an element of
S1
> > etc. They ARE ORDERED LEFT TO RIGHT. Am I misunderstanding something
or is
> > there some other mathematical definition of "relation" that is the one
on
> > which relational database theory is based?
>
> A tuple is a set of ordered pairs of the form (attribute, value).
> Defining an ordering for the attributes would be superfluous.
>
> URL:http://en2.wikipedia.org/wiki/Ordered_pair

So a tuple is NOT ordered? Why not? Why even call an unordered set a tuple? Tuples imply ordering, right? They are elements of Set1 x Set2 x Set3 x ... Setn. It is fine with me if you want those sets to be sets of ordered pairs -- they can be sets of whatever, but the relation is then a set of tuples (s1, ... sn) where s1 is an element of S1 (and in your def, that means it would be an ordered pair).

But a RELATION itself is a set of ORDERED TUPLES -- RIGHT? Else please point me to a MATHEMATICS definition that allows for relations that are not ordered. I'm not finding any such definitions.
>
> You have much to unlearn, Grasshopper.

Ditto, methinks. Smiles. --dawn

>
> --
> Joe Foster <mailto:jlfoster%40znet.com> On the cans?
<http://www.xenu.net/>
> WARNING: I cannot be held responsible for the above They're
coming to
> because my cats have apparently learned to type. take me away,
ha ha!
>
>
Received on Fri Dec 26 2003 - 22:17:20 CST

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