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

"Cimode" <cimode@xxxxxxxxxxx> wrote in message
news:1185468975.337120.62330@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On 26 juil, 18:21, "Bruce C. Baker" <b...@xxxxxxxxxxxxxxxxxxxxxxx>
wrote:
"Cimode" <cim...@xxxxxxxxxxx> wrote in message

news:1185462964.626601.174460@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx



On 26 juil, 16:38, "Bruce C. Baker" <b...@xxxxxxxxxxxxxxxxxxxxxxx>
wrote:
"Cimode" <cim...@xxxxxxxxxxx> wrote in message

news:1185446387.854491.306850@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

On 26 juil, 03:13, "Bruce C. Baker" <b...@xxxxxxxxxxxxxxxxxxxxxxx>
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?

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).



.

Relevant Pages