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

Date: Thu, 26 Jul 2007 16:58:09 -0300
Message-ID: <46a8fca4\$0\$8833\$9a566e8b_at_news.aliant.net>

> "Cimode" <cimode_at_hotmail.com> wrote in message
>

>>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 ... :-)

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. Received on Thu Jul 26 2007 - 21:58:09 CEST

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