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Re: Grammatical Inconsistencies

From: Timothy J. Bruce <uniblab_at_hotmail.com>
Date: 23 Apr 2004 10:42:28 -0700
Message-ID: <34519632.0404230942.c6067d8@posting.google.com>


[...It's morning all right]

> 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

Let us have the sets A, B, and C, where A = {1, 2, 3, 4} and B = {chicken, cat, dog, cow}.
Let relation F be a subset of the cartesian product of sets A and B, that is F is a subset of A x B, such as {(1, chicken), (2, cat), (3, dog), (4, cow)}.
Let relation G be a subset of the cartesian product of C and no other sets, such that C = {(1), (4)}.
If relation F was the predicate `Animals I own', and relation G was the unary predicate `Animals of which I own I like to eat', the notion of `I like to eat 1' does not make any sense. If we define G.C as a subset of F.A (that is a fairly good definition of FOREIGN KEY, btw), we are on the right track, but still not finished. We would like the phrase `I like to eat chicken' in place of `I like to eat 1'. The most obvious solution is to perform a join of some sort against relations F and G, and by doing so we are concerned with the _INTERSECTION_ between sets A and C (specifically sets F.A and G.C), and then performing a projection of relation F. This is no doubt the source of confusion in the matter. We join relations by performing an intersection, union, or symetric difference on attributes (read: sets) of those relations and performing a projection on the relations in question.

I have, on occasion, suggested to someone `Intersect relations A and B via relation C' (which may have amplified this obviously confusing matter), in an informal instruction of how to solve for many-to-many relationships between relations A and B. It is not the relations themselves, per sť, which are being intersected, but the sets (specifically the keys) which are in consideration.

Just as I `nit-picked' you, Leffler will no doubt `nit-pick' me. I consider this a _welcome_ event and look forward to it an opportunity for any needed correction.

Do yourself a favour and read the Grimaldi's book, Timothy J. Bruce
uniblab_at_hotmail.com
</RANT> Received on Fri Apr 23 2004 - 12:42:28 CDT

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