# Re: Grammatical Inconsistencies

Date: Fri, 23 Apr 2004 17:16:14 +0300

Message-ID: <40892481$1_at_post.usenet.com>

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"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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