Re: x*x-1=0

In article <94gv2l$c38$1_at_news.tue.nl>,   hidders_at_win.tue.nl (Jan Hidders) wrote:
> >
> > 0 = empty set
> > 1 = {0}
> > 2 = {0,1}
> > sorry for been off topic here.
>
> I don't really see anything wrong with that as long as you keep in
> mind that you are just defining a model of the numbers. Statements
 like
> 1 is really just singleton 0 make me always slightly cringe. :-)

It is probably fine with 1, as there is seemingly no other way to define it:-) It is "2" where things become ambiguous: alternative definition of "2" is {1}. Also, this construct is no help as far as algebraic operations are concerned.

> But to get back on topic; historically the set interpretation comes
> before the algebraic equalities. The latter are usually just regarded
> as a nice bonus that enables you to do query optimization.
>
> > > RENAME is not really neccesary if you simply assume that your
 tables
> > > contain simple tuples like <a,"harry","12-3-52"> without column
 names.
> >
> > A newbie question here: how do we join tables without column names?
>
> You don't need the joins because they can be simulated with the
> (relational) cartesian product followed by a selection and a
> projection.

True. The question then is about selection. I'm confused about notation. Perhaps some example would help.

> But things get, from an algebraic perspective, a little
> more complicated because the cartesian product does not commute as the
> join does.

? (Here I'm illiterate again:-)

>
> And that also tells how a join can be defined on bags because it will
> be similar to the cartesian product on bags. So if a tuple occurs n
> times in a table and is joined with another tuple in another table
 that
> appears there m times, then the joined tuple will appear n*m times in
> the result. And that gives an idea of what will happen if you also
> assume that your equation has a solution: you will get "complex bags"
> that may contain a tuple i times where i is the complex number such
> that i^2 = -1.

Here I feel like I'm tricked up. All that has been done at this point is classic algebraic number extension only. It is not extension in terms of relational operations. It would be a nice discovery if you can prove that we don't need any relational specific extensions. (In classic algebra any new operation extended number field, why relational counterpart differs?)

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http://www.deja.com/ Received on Mon Jan 22 2001 - 19:06:35 CET