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

Date: Thu, 26 Jul 2007 10:21:56 -0700

Message-ID: <1185470516.361420.161720_at_w3g2000hsg.googlegroups.com>

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
**>
**> >news:1185462964.626601.174460_at_d55g2000hsg.googlegroups.com...
**>
**> > > On 26 juil, 16:38, "Bruce C. Baker" <b..._at_undisclosedlocation.net>
**> > > wrote:
**> > >> "Cimode" <cim..._at_hotmail.com> wrote in message
**>
**> > >>news:1185446387.854491.306850_at_w3g2000hsg.googlegroups.com...
**>
**> > >> > 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