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From: "Mikito Harakiri" <mikharakiri_nospaum@yahoo.com>
Newsgroups: comp.databases.theory
Subject: Re: How can I proove associtivity of natural in relational algebra?
Date: 22 Nov 2005 09:14:09 -0800
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Filter911 wrote:
> Mikito Harakiri wrote:
> > Filter911 wrote:
> > > Mikito Harakiri wrote:
> > > > Filter911 wrote:
> > > > > Can someone give me a link for a full proof or something?
> > > >
> > > > Given relations A,B, and C, expand each realtion into a (possibly
> > > > infinite) relations A', B', and C' with the same set of attributes
> > > > (which is the union of the attribute sets for A, B, and C). Then, the
> > > > join of A, B and C is the intersection of A', B', and C'. Intersection
> > > > is associative.
> > >
> > > What do you mean by "expand each relation"?
> >
> > "Extend", is the opposite of "project". E.g. the relation with a single
> > attribute
> >
> > A = {(a=1), (a=2)} is exended to the attribute set {a,b} with the
> > domain of attribute b being {7,8,9} as
> Extanding using what? Using B or C? or some new relation? any full
> example or link?
> If I use the union of the three then A=B=C and that's a prviate case

Find the set of all attributes in B and C which are not in A. Get
cartesian product of their respective domains. Cartesian product it
with A. This is how you get A'.

The other hint. Start with cartesian product (which is associative),
and show that selection doesn't affect associativity.