Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?
Date: Fri, 14 Feb 2003 13:05:21 -0800
"Steve Kass" <skass_at_drew.edu> wrote in message
> >I don't agree that the matter is "context dependent". One either has a
> >with a consistent set of operations that users like, or not.
> Whether "users like" something has nothing to do with its mathematical
But a successful theory is the one that is adopted by the users:-)
> Because of its use for sets, intersect (I think) gives the impression
> of, well, intersection, not product. I just don't see why you'd call
> the operation defined by f op g (x) = f (x) * g(x) "intersect" instead
> of product.
If "*" operation works like this
0*0=0 0*1=0 1*1=1
then it can be called intersection, even though it gives
Intersection is a product!
> >More concisely:
> >PROJECT*POWER != 1
> Right. But there's no problem here, just as there's no problem
> with the fact that matrix multiplication is not commutative, even
> though matrices can be considered a generalization of a set where
> the multiplication is commutative.
I don't see how matrices can be viewed as generalization of sets. Matrices are Linear Transformations, not sets.
On the other hand, you may be right. Projection is defined as an operation that obeys the following law:
PROJECT * PROJECT = PROJECT There is no conlict between this and the above PROJECT*POWER != 1.
In general, the whole issue about sets vs. bags might be not important. What if we dismiss tuples altogether? Math frequently takes an operational approach, when we are agnostic about the nature of the space and are only concerned with space transformations. "Tell me what operations you have and what laws do they obey, and I might cook some interpretation for you". Received on Fri Feb 14 2003 - 22:05:21 CET