Re: The MySQL/PHP pair

"Dawn M. Wolthuis" <dwolt_at_tincat-group.comREMOVE> wrote in message news:<cmaqq2$a1h$1_at_news.netins.net>...
> "Dan" <guntermann_at_verizon.com> wrote in message
> news:Kg0id.6107$wP1.5011_at_trnddc09...
> >
> > "Dawn M. Wolthuis" <dwolt_at_tincat-group.comREMOVE> wrote in message
> > news:cm93fd$g11$1_at_news.netins.net...
> > > "erk" <eric.kaun_at_pnc.com> wrote in message
> > > news:1099431388.630616.174500_at_f14g2000cwb.googlegroups.com...
> >
> >
> > [snip]
> > >
> > > It makes sense to bring it up since I have yet to PROVE all of my
> > > concerns.
> > > I have proven, I think, that 1NF as currently implemented by most
> software
> > > developers (the old version of 1NF) has no mathematical basis.
> >
> > What is this proof, pray tell. I've asked for a demonstration already
> where
> > attributes of a relation are anything less than an elements in the
> > mathematical or logical sense when operated upon by relational operators.
>
> If you go back to the original Codd papers and look at the definitions of
> relation and normalization, you can see that, as Codd acknowledges, there is
> nothing in the mathematics that prohibits relations (or functions, bags,
> sets, ...) as elements of relations.

As long as you refer to functions, bags, sets, etc. as only as elements from the relational perspective. In other words, such terms as functions, bags, etc don't exist in the relational model. This implies that intrinsic sub-elements/components of these specific types should not be directly accesible or manipulated across one another from the perspective of a relational system (We can call it the relational layer for those of you starry-eyed from a layered architectural approach).

Here is my understanding of a precise mathematical definition of a binary relation (incidentally I asked this from you over the months). The definition of an n-ary relation can be extended from this.

a R b <-> (a,b) e R

I see no conflict between this mathematical definition and what Codd originally demonstrated as part of the definition of a relational model. The mathematical definition is decidedly first-order. On the other hand, I see conflicts with this mathematical definition and with what you espouse, if I am correctly interpreting what you have been saying.

• Dan