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

From: Bob Badour <bbadour_at_pei.sympatico.ca>

Date: Thu, 26 Jul 2007 16:58:09 -0300

Message-ID: <46a8fca4$0$8833$9a566e8b_at_news.aliant.net>

>>On 26 juil, 18:21, "Bruce C. Baker" <b..._at_undisclosedlocation.net>

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