# Re: I think my book may be wrong about cardinality, but I'm not sure

From: JOG <jog_at_cs.nott.ac.uk>
Date: Thu, 26 Jul 2007 10:21:56 -0700

On Jul 26, 5:56 pm, Cimode <cim..._at_hotmail.com> wrote:
> On 26 juil, 18:21, "Bruce C. Baker" <b..._at_undisclosedlocation.net>
> wrote:
>
>
>
> > "Cimode" <cim..._at_hotmail.com> wrote in message
>
>
> > > On 26 juil, 16:38, "Bruce C. Baker" <b..._at_undisclosedlocation.net>
> > > wrote:
> > >> "Cimode" <cim..._at_hotmail.com> wrote in message
>
>
> > >> > On 26 juil, 03:13, "Bruce C. Baker" <b..._at_undisclosedlocation.net>
> > >> > wrote:
>
> > >> <snip>
>
> > >> >> Each tuple in a relation with N attributes corresponds to a point in
> > >> >> an
> > >> >> N-dimensional space, with each attribute being orthogonal to all of
> > >> >> the
> > >> >> others.
> > >> > What does that mean ? How is a single attribute orthogonal to N-1
> > >> > attributes part of the same relation?. What do you exactly designate
> > >> > as *orthogonality*? Why would a tuple necessarily be a point and not
> > >> > a line ofr plane in geometrical N-space?
> > >> > What about degree 0/1 relations? How does a degree 0 relation
> > >> > represent a point in space?
>
> > >> The answers to all your questions can be found in any linear algebra
> > >> textbook.
>
> > > Really? Would you care providing a source?
>
> > "If a relation has /n/ columns, then /each row in that relation represents a
> > point in n-dimensional space/--and the relation as a whole represents a set
> > of such points. In other words, a relation of /n/ columns is
> > /n/-dimensional, not two-dimensional. *Let's all vow never to say "flat
> > relations" ever again.*"
>
> > "Date on Database", ISBN 1-59059-746-X, page 371
>
> > As for a linear algebra textbook, there are thousands of them. Pick one and
> > make the necessary extrapolation to relational database theory.
>
> That's what I suspected (Date's algebra).
>
> Thank you anyway for providing some sources (I do appreciate the
> effort). The purpose of my questions was to raise the issue that one
> may *arbitrarily choose several math constructs to describe the *non
> flat* nature of relations. Choosing a POINT in N dimensionnal space
> (correlated to N attributes) to describe relation tuple set is just
> one *possible* math construct choice and such choice has implications
> I never felt confortable with. If I apply Date's definition replacing
> the *n* by some values:
>
> > A degree 1 relation tuple set is necessarily a LINE (1 - dimensional space)
> > A degree 2 relation tuple set is necessarily represented as a PLANE (2 - dimensional space)
> > How is a degree 0 relation tuple set represented considering that it has 0-dimensions according to Date?

A section discussing 0-dimensional space from the wikipedia entry on the famous "Flatland: A Romance of Many Dimensions":

"He then has a dream in which the Sphere visits him again, this time to introduce him to Pointland (which comprises a self-aware point that occupies all space and knows nothing but itself). The point (sole inhabitant, monarch, and universe in one) perceives any attempt at communicating with him as simply being a thought originating in his own mind."

>
> I have read Date's and I was in fact hoping for some pointers on this
> specific issues. I have not found anything yet on that subject (yet).- Hide quoted text -
>
> - Show quoted text -
Received on Thu Jul 26 2007 - 19:21:56 CEST

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