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

From: Cimode <cimode_at_hotmail.com>
Date: Thu, 26 Jul 2007 09:56:15 -0700

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?

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