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Re: Grammatical Inconsistencies

From: x <x-false_at_yahoo.com>
Date: Fri, 23 Apr 2004 17:16:14 +0300
Message-ID: <40892481$1@post.usenet.com>

"Dawn M. Wolthuis" <dwolt_at_tincat-group.com> wrote in message news:c697n2$fis$1_at_news.netins.net...
> OK -- I thought all of these operations were on relations and returning
> relations.

> Are you willing to bother showing me an example of the use of a join
within
> the relational theory framework where it is not the same as the
> cross-product -- or pointing me to some such example? I suppose I'm
pushing
> my luck, eh?
> --dawn

Upon my knowledge CARTESIAN PRODUCT always means UNRESTRICTED PRODUCT of SETs
A "RELATION" is a particular kind of SET (a subset of some CARTESIAN PRODUCT).
A "RELATION" often is a RESTRICTED PRODUCT of some SETs. The JOIN of two RELATIONs is always a RELATION thus it is not a CARTESIAN PRODUCT. Suppose A , B and C are sets and r1 is a subset of AxB , r2 is a subset of BxC.
Then :
a) r1 JOIN r2 is a SUBSET of AxBxC
b) r1 CARTESIAN PRODUCT r2 is a SUBSET of AxBxBxC One may think r1 CARTESIAN PRODUCT r2 is a RELATION whose domains are A, B, B and C.
But AxBxC is not the same thing as AxBxBxC...

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Received on Fri Apr 23 2004 - 09:16:14 CDT

Original text of this message

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