Re: How can I proove associtivity of natural in relational algebra?
Date: 21 Nov 2005 13:35:53 -0800
Message-ID: <1132608953.263060.39140_at_g44g2000cwa.googlegroups.com>
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
A' = {(a=1, b=7),(a=1, b=8),(a=1, b=9),(a=2, b=7),(a=2, b=8),(a=2,
b=9))}