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

From: Bruce C. Baker <bcb_at_undisclosedlocation.net>
Date: Thu, 26 Jul 2007 14:03:02 -0500
Message-ID: <Lc6qi.1997\$Uz4.1283_at_newsfe19.lga>

"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
>> 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).
>
```
Received on Thu Jul 26 2007 - 21:03:02 CEST

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