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Home -> Community -> Usenet -> comp.databases.theory -> Re: Grammatical Inconsistencies
"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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