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

Date: Thu, 26 Jul 2007 09:56:15 -0700

Message-ID: <1185468975.337120.62330_at_d55g2000hsg.googlegroups.com>

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?
*