Re: The Fact of relational algebra (was Re: Clean Object Class Design -- What is it?)

"Bob Badour" <bbadour_at_golden.net> wrote in message news:AJHv7.668$5X7.18802717_at_radon.golden.net...
> > I seem to remember the rdbms guys redefined 'completeness', to something
> > that has no bearing on mathematical compeletness (which I cant remember
> the
> > definition of anymore).
>
> "Seem to", "I can't remember"... Would you like to argue against something
> you know and can remember? It might prove a little more useful.

er.. Im not arguing, Im discussing ;-)

> By any chance, are you referring to the difference operator vs. set
> negation? One uses an explicit finite universe and the other uses an
> implicit potentially infinite universe.

Youve lost me there.

> > I mean, mechanical engineers use applied mathematics
> > to underpin their theories, but they don't go an redefine fundamental
> > concepts on a whim! So why do computer scientists do that???
>
> I doubt that mechanical engineers have much use for infinite in their
daily
> jobs when applying mathematics. Recalling from my own electrical
engineering
> background, such singularities only proved useful in frequency filter
> design.

Engineers seem to use mathematics to communicate. In computer science they seem to use mathematics to create walls. Maybe thats just how it seems at the moment. It would be good if everyone had some knowlege of set theory. Then you could 'kick down' into set theory if you wanted to express something more rigorously. Insead we have the 'relational model' which is fine, but not very good as a method of communication, and we have all sorts of diagramming techniques which are very good for communication, but aren't very rigourously defined.

> > But I think its kind of important. I think you could re-implement
> relational
> > algebra with identity based semantics.
>
> Values are identity, which obviates the need for re-implementation.

Values are not identities. Vaules are only unique in their domain. For example, each member of the 'Set of all employee keys', is unique only in that set.
E = set if employees
D = set of departments
Ek = set of employee keys
Dk = set of department keys

| E or D | /= | Ek or Dk |

> > I think it would be a lot closer to
> > set theory then. Set theory is what people use to 'implement'
mathematics
> > these days ;-)
>
> I think you will find that the attempt ran into limitations.

It certainly did, it it is irrelevent to us anyway. Set theory still remains the basic language that mathematitians seem to use (in my limited experience anyway).

Cheers

Daniel Received on Tue Oct 09 2001 - 11:16:14 CEST