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 16:10:06 -0500
Message-ID: <Q48qi.9292$lZ7.8018_at_newsfe20.lga>


"Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message news:46a90c7e$0$8837$9a566e8b_at_news.aliant.net...
> Bruce C. Baker wrote:
>
>> "Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message
>> news:46a8fca4$0$8833$9a566e8b_at_news.aliant.net...
>>
>>>Bruce C. Baker wrote:
>>>
>>>
>>>>"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
>>>>>>
>>>>>>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?
>>>>
>>>>
>>>>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 ... :-)
>>>
>>>Not null. True. A non-empty 0-ary relation is the relational equivalent
>>>of True. An empty 0-ary relation is the relational equivalent of False.
>>
>> Allow me to correct a poor word choice in my previous post: When I wrote
>> NULL, I was thinking along the lines of a null reference, as in C or C#,
>> NOT a SQL NULL.
>>
>> I think I see where you're going with True and False as defined in your
>> post, though ...
>
> It's not so much where I am going as it is where the relational folks have
> already gone. In particular D&D.

In the Third Manifesto, 3/e?

I've dipped into the book but I can't say I've studied it in depth.

Yet another item for the TODO list! :-| Received on Thu Jul 26 2007 - 23:10:06 CEST

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