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

"Neo" <neo55592_at_hotmail.com> wrote in message news:4b45d3ad.0305041458.14afcf9b_at_posting.google.com...
> > A (binary) relation is a subset of a Cartesian product.
>
> Yes, you are in synch with text books.
> Schaum's Outline explains 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.

To expand on the comparison a little:

An example of a binary relation on Z x Z (the integers) is 'less than'. So the set of all integers a, b where a < b is a binary relation. If your explanation of the standard definition were correct, (which I do understand you specifically disagree with) then we would say '1<2' and '7<123' are binary relations.

> They will have to rewrite the books and take back some diplomas or
> more likely they will keep the current inaccurate definitions which
> makes my experience on google all the more interesting :)

It might be better, if you want to create a new math, to create your own terms as well, rather than redefine existing terms. That just confuses people, and causes lots of arguments about definitions.

Marshall Received on Mon May 05 2003 - 02:25:50 CEST