Re: Relation subset operators

cimode_at_hotmail.com wrote:
...
> In a way that gave to think that relational model is *not* ready yet
> to apply absurd mathematical reasonning yet. Be it finally sound or
> not, absurd logical reasonning is too risky for a young science to be
> used as a foundation . I will stick to basic clarifications on a step
> y step basis and let the big theories to smarter people.
> ...

No argument with that, but if we're talking about a shorthand for division, which is universal quantification, which is defined in fopc, then the shorthand should produce an equivalent answer to fopc, eg., as Date says:

(quote)
Have you ever wondered why the operation is called "division?" The following identity shows why:

( R TIMES S ) DIVIDEBY S = R Division is a kind of inverse of Cartesian product, and it isn't quite the counterpart to the universal quantifier that it was meant to be. It suffers from problems having to do with empty sets and related matters.6 In fact, Codd offers an example that illustrates the problem: Given a relation SP { S#, P#, ... } showing which suppliers supply which parts, he claims that the expression SP { S#, P# } DIVIDEBY SP { P# } will give numbers for suppliers who provide all parts. However, if there aren't any parts, this expression gives the wrong answer. (It gives no supplier numbers, yet it should give them all).

Relational comparisons provide a better basis for dealing with the kinds of problems that division was intended to solve -- but the relational model as originally defined by Codd didn't include such comparisons at all.7
(end quote)

(I'm distinguishing shorthand from shortcut, one saves typos', the other saves steps.) Received on Sat Jun 06 2009 - 20:02:25 CEST