Re: x*x-1=0

From: Vadim Tropashko <vadimtro_at_yahoo.com>
Date: Sun, 21 Jan 2001 17:46:21 GMT
Message-ID: <94f79c$ov7$1@nnrp1.deja.com>

> > > Assuming that this equation is solveable leads to the peculiar
> > > property that there will be sets that you can add a non-empty set
> > > to such that the result will be an empty. You might call them
> > > "negative sets" if you will.
> >
> > This is a discovery of negative tables/sets, right? (We are in the
 very
> > beginning, therefore, of the classic sequence
> > negative->rational->complex numbers:-)
>
> Sort of. Perhaps you could treat them as some kind of generalized bag
> where a bag can contain an element -3 times. I doubt if that is
> really a new idea.
>

OK. We assign a weight to each element. Is there a definition of joint operation upon such things?

> > Still something is not quite right here, and until things would be
> > cleaned up we cant expect those to be good concepts. Things that
> > bother me:
> >
> > 1. DUM (or '0') - is is a table with no rows an columns only (i), or
> > any table with empty set of rows (ii)?
>
> It is both because both tables are simply the empty set.
>

I'm kind of uneasy about set reductionism. This reminds me unfamous

0 = empty set
1 = {0}
2 = {0,1}

sorry for been off topic here.
> > 2. Column name renaming. Some equations wouldn't have any solutions
> > simply because column name signatures are different, so we need some
> > identities here as well. Here operator RENAME is very confusing. Are
> > we allowed to insert this operator into any part of the equation to
> > "sweeten" the solution (othervise it might bail out on trivial
> > signature mismatch?) BTW, is RENAME a true relational operator that
> > should be added to grand five? I'm personally more happy if it's
> > possible to define some table identities based on table header
> > signatures alone, and drop RENAME altogether.
>
> 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? (first rule of relational -- verify everything against joints:-)

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http://www.deja.com/ Received on Sun Jan 21 2001 - 11:46:21 CST