Re: I think my book may be wrong about cardinality, but I'm not sure
Date: Thu, 26 Jul 2007 14:03:02 -0500
"Cimode" <cimode_at_hotmail.com> wrote in message news: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
>> > 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
>> 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
>> 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
>> 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?
Good point! (Please excuse the pun; an opportunity like this arises only once in a lifetime. :-) )
What /does/ an empty tuple represent? Is it some sort of NULL, as opposed to a null /set/?
And since the tuples in a relation must all be distinct, that would seem to imply that a non-empty relation having no attributes could contain only a single "null tuple". Could this "null relation" serve as an identity element for joins?
Let me get back to you ... :-)
> > 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). >Received on Thu Jul 26 2007 - 21:03:02 CEST