Re: Base Normal Form

Marshall Spight wrote:
> dawn wrote:
> > [a lot of stuff]
>
> Dawn,
>
> Uh, wow.

Glad you enjoyed? :-)

> I don't *want* to ditch the word relation; I don't have another
> word that comes close. "Function" doesn't cut it.

Because ... ? Granted, it is but one way to model data. I don't insist on a single way of viewing the subject. However, I can discuss the topic of data modeling quite thouroughly without ever using the term "relation" but not without using the term "function".

> I also
> don't see any particular conflict or even a difference between
> mathematics and computer science; I consider CS to be a branch
> of math, with some particular areas of emphasis, such as
> how much work calculating a particular function is.

So one might hope that CS would not take a solid, generally agreed upon, mathematical term and redefine it. But that does seem to be what has happened, unfortunately.

> And what's wrong with "a subset of the product of sets?" That's
> not all that complicated.

I like it. I haven't seen a product of sets that has unordered "columns" however.

> It's no more complicated than "a mapping
> from one set to another."

Functions are a subset of relations that is a little easier to teach, however. In kindergarten the students match an item on the left hand side of the page to exactly one on the right before any exercises that permit the more generalized form of a relation, allowing an item on the left to have a line to more than one item. So, I would argue that there is some slight advantage to introducing the concept of a function and then generalizing instead of starting with relations and then narrowing it down.

>
> > > It doesn't have to be required, it usually follows from the fact that
> > > the relation is a set.
> >
> > You lost me here. How do you define a candidate key in mathematics so
> > that every set must have one?
>
> A "set" is a collection of *unique* members. Because of that word
> "unique" there has to be a candidate key.

OK, I'm with you and willing to hit my forehead and say "duh". Saying that because something is a set it must be a function is not accurate, but, yes, there is a function that can be associated with any set. If no subset of the element/tuple variable is a candidate key, then the entire element would be. Sorry I missed the point. --dawn Received on Tue Jul 12 2005 - 22:06:04 CEST