Re: x*x-1=0

Vadim Tropashko wrote:
> In article <94mhpf$jdh$1_at_news.tue.nl>,
> hidders_at_win.tue.nl (Jan Hidders) wrote:
> > Note that if you have ordered tuples then the projection is also
> > likely to be slightly different. If you say PROJ[#1,#2](R) then
> > that will mean something else than PROJ[#2,#1](R).
>
> What are unordered tuples: sets or bags?

Neither. The tuples are the elements of the sets and bags. Whether you allow an element to occur more than once inside a collection determines if it is a set or a bag.

> > > I disagree that CP = MULTIPLY, and, in general, that order of
> > > columns matters. This is why I wanted some congruences on tuples.
> >
> > You cannot disagree, it is just a matter of definition. :-) And
> > whether CP = MULTIPLY depends an how you define MULTIPLY and that
> > you didn't do yet.
>
> Well, I meant definition from Chris Date's textbook.

Oh? What version are you reading? In mine he calls it the product.

> It might look less rigorous than CP defined on tuples, but it
> captures one important concept that tuple theory is missing --
> domains. In this context CP =/= MULTIPLY, right?

Sorry, but no. Having domains or not has nothing to do with it; you can also have them with ordered tuples. The only difference is that the name of the fields (or columns, if you will) are replaced with numbers. This is often done in theoretical treatments of the algebra because you get basicaly the same algebra but without the renaming operation.

-- 
  Jan Hidders