Re: Do Data Models Need to built on a Mathematical Concept?

"Neo" <neo55592_at_hotmail.com> wrote in message news:4b45d3ad.0305050743.30acb4de_at_posting.google.com...
> > > Pg 65 of Schaum's Outline (0-07-038159-3), binary relation as follows:
> > > A = (b,c)
> > > B = (j,k,l)
> > > AxB = ((b,j), (b,k), (b,l), (c,j), (c,k), (c,l))
> > > then (b,j), (b,k) ... are binary relations.
> >
> > That's not the generally accepted definition of the term. Nor is it even
> > what that specific book says; I checked. What is says is:
> > "Let A and B be sets. A *binary relation* or, simple,
> > a *relation* from A to B is a subset of A x B."
> > So, to fix your example, the cardinality-2 set { (b,j), (b,k) } is
> > a binary relation.
>
> Ok, let me try to understand:
> "A *binary relation* from A to B is a subset of A x B."
> Since (NULL) is a subset of AxB, it is a binary relation!!!
> Since ((b,j)) is a subset of AxB, it is a binary relation.
> Since ((b,j), (b,k)) is a subset of AxB, it is a binary relation.
> Since ((b,j), (b,k), (b,l)) is a subset of AxB, it is a binary
> relation.
> and so on....

Exactly so.

> If the above is the correct interpretation, I find the definition to
> be inaccurate in that ...

It doesn't really make much sense to discuss whether a definition is "accurate" or not. A definition is when we put a name on a thing. In fact, we sometimes say something is true "by definition."

> it has not defined the fundamental form of a
> binary relation.

I still think you're going to be better off coming up with your own term for the thing you're trying to capture, rather than trying to reuse the exact form of a popular mathematical term. Pretty much everyone who hears you say "a binary relation is [some thing you want to say about your ideas]" is just going to think that you aren't sufficiently educated in math. How are they to tell that you're not using the accepted definition incorrectly, but are instead describing your own term? The easy way for them to tell is if you use a term they haven't seen before.

> However, I think I see where my perceptions mismatches or errors from
> that of the rest. The rest see three nodes and TWO links as a binary
> relation, the rest count relations. I have been calling TWO nodes and
> one link a binary relation, I counted things. Is this where my mistake
> lies?

I kind of think it has to do with an element-at-a-time view vs. a set-at-a-time view.

Marshall Received on Tue May 06 2003 - 03:47:57 CEST