Dee Dum

VC wrote:
> "Vadim Tropashko" <vadimtro_invalid_at_yahoo.com> wrote in message
> > In D&D algebra
> >
> > A union DEE != A
> > A union DEE != DEE
> > A join DEE = A
> >
> > A union DUM = A
> > A join DEE != DEE
> > A join DEE != A
>
> But in your algebra:
>
> A union DEE = DUM
> A join DEE = A
>
> A union DUM = DUM
> A join DUM= 'a0'

Let's be a little bit pedantic, and refer to DEE and DUM as elements of D&D algebra, while defining 10 as a join of all the elements (the greatest element) and 01 as a union of all the elements (the least element). Then,

01 < A < 10

for any A. Hence, the two inequalities rewritten as 4 identities

01 join A = A
01 union A = 0

10 join A = 10 (corrected:-)
10 union A = A

It was precisely this set of identities that I losely compared with DEE and DUM identities in the D&D algebra. Although, this comment is just a reiteration of the lack of symmetry in D&D algebra that has been already discussed. (The incompatibility of the order relations imposed by the upper and lower semilattice).

Now, the 00 element is a whole different story. It is not comparable to any element in the lattice except the header and rowid relations. Hmm... How to define it formally? Received on Wed Aug 17 2005 - 18:46:54 CEST