Re: Database design

From: x <x_at_not-exists.org>
Date: Thu, 23 Feb 2006 15:25:04 +0200
Message-ID: <dtkd3k$hi2$1_at_emma.aioe.org>


"Alexandr Savinov" <spam_at_conceptoriented.com> wrote in message news:43fdab16$1_at_news.fhg.de...
> x schrieb:

> >> We can build a non-flat space if assume that coordinates are
> >> themselves points with their own coordinates.
> >
> > Nobody stop you to do that in the RM.

> Yes, using RM we can implement a non-flat (hierarchical space).
> (And not only this, but also graphs and many-many other structure.)
> But the question was what we can implement using only one table. That
> the statement was that one table is flat.

Yes. One relation.

> >> Alternatively, we
> >> can continue this space hierarchy in the opposite direction (upward).
> >> The points from this set can be used as coordinates for points from
> >> another set. Those points can again be used as coordinates.
> >
> > Nobody stop you to do that in the RM.

> Yes, RM is powerful and flexible enough to model such structures. But
> the question is if one table can do that.

Yes. One relation.

> >> So we call a structure flat if it can be shown equivalent to a
> >> n-dimensional space (without a hierarchy).
> >
> > You call it so. I have not seen a formal definition.
> > A relation is not equivalent to a n-dimensional space.
> > Please define the equivalence relation.
>
> I already defined. Here it is again:

> Domains = Axes
> Values = Coordinates
> Points = Records
> Relation = N-dimensional space

This is not an equivalence relation.
A relation is a [strict] subset of a N-dimensional space.

> > What do you mean by "an n-dimensional space is without hierarchy" ?
> >
> > Product
> > Vendor p1 p2 p3
> > v1 c1 c2 c3
> > v2 c4 c5 c6
> >
> > has at least two hierarchies:
> > Vendor --> Product
> > Product--->Vendor

> Implicitly you assume the existence of two tables while we are talking
> about one table only.

The above is one n-dimensional space *with* 2 hierarchies. You said a n-dimensional space is *without* hierarchy.

>With tables you can model two levels.
>With more tables you can model more levels (or more dimensions - it
depends how
> you arrange and interpret them).

With one relation with n attributes I can model at least n! hierarchies.

> So again, the question is what can we model with a single table.

Why ? Nobody restrict you to use a single relation.

>Since the number of levels is limited we could find it natural to call
such a
> structure flat. That is all.

It is flat by definition. You defined it to be flat. Received on Thu Feb 23 2006 - 14:25:04 CET

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