Re: x*x-1=0

In article <958n31$4g2$1_at_news.tue.nl>,   hidders_at_win.tue.nl (Jan Hidders) wrote:
> Vadim Tropashko wrote:
> > In article <94rr74$l4j$1_at_news.tue.nl>,
> > hidders_at_win.tue.nl (Jan Hidders) wrote:
> > > Vadim Tropashko wrote:
> > > > Do tuples have *internal* structure in terms of set/bags theory?
>
> Yes, named tuples are defined as functions that map a name to a value.

I'm OK with this definition.

> And, as you probably know, functions can again be defined as a set of
> pairs, and a pair can also be defined in terms of sets.

Here, Reductionalism, again! A pair is defined in terms of sets as {a, {b}} or as {{a}, b}. This ambiguity indicates that the set construction is far from perfect. (At least, in programming ambiguity was never a good thing:-)

> > > > > But things get, from an algebraic perspective, a little more
> > > > > complicated because the cartesian product does not commute as
> > > > > the join does.
> >
> > In exercise 6.1 Chris suggests to verify that product (along with
 some
> > other operations) is commutative. On the other page he claims that
 join
> > is commutative as well.
>
> Yes, but note that he talks about the algebra defined on sets of
> *named* tuples (and, therefore, needs the rename operator) where I was
> talking about the algebra defined on sets of *ordered* tuples. The
> operations on these algebras are similar but have different algebraic
> properties.
>
> > I agree that renaming could be viewed as algebraic operation. I
 wonder
> > 1. if this is a productive definition
>
> Well, for starters, it is definitely something that you need to be
 able
> to do, and it is not expressible with the other operators. So by that
> definition of "productive" it is not only productive but even
 inescapable.
>
> > 2. how would I define relational algebra without renaming (renaming,
> > then, goes into metamodel). The fact that in classic algebras we
 never
> > consider renaming as part of algebra confuses me
>
> Sorry, renaming has to be there. That it confuses you is not the
> algebra's problem. :-)
>
> > 3. how algebra with renaming operation relates to the one without it
>
> The expressive power becomes greater.

For me this sounds pretty much like "If I rename variables in Maxwell equations, then they won't describe electromagnetic waves any more".

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http://www.deja.com/ Received on Wed Jan 31 2001 - 20:39:27 CET