Re: Base Normal Form

From: Marshall Spight <marshall.spight_at_gmail.com>
Date: 12 Jul 2005 20:29:37 -0700
Message-ID: <1121225377.824884.11790_at_g44g2000cwa.googlegroups.com>


dawn wrote:
> Marshall Spight wrote:
> > dawn wrote:
> > > [a lot of stuff]
> >
> > Dawn,
> >
> > Uh, wow.
>
> Glad you enjoyed? :-)

let's say I was engrossed.

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

For one thing, in my field, the term 'function' has a strong connotation of being intentional, and relation has a strong connotation of being extentional. enough so that if I mean the other kind of each I explicitly specify.

> > 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.

It doesn't look much that way to me. And if it had, what would be the problem? words change meaning as they move from one field to another all the time.

> > 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.

the product operation on integers and on relations is commutative, so I don't see any basis for describing the operands of either as ordered.

> > 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.

I respect that you have pedagogical issues to deal with but I don't see that they are relevant here.

Marshall Received on Wed Jul 13 2005 - 05:29:37 CEST

Original text of this message