Re: Distributivity in Tropashko's Lattice Algebra
Date: 17 Aug 2005 10:55:19 -0700
Message-ID: <1124301319.179336.74200_at_g43g2000cwa.googlegroups.com>
VC wrote:
> "Mikito Harakiri" <mikharakiri_nospaum_at_yahoo.com> wrote in message
> news:1124225375.601615.162210_at_g47g2000cwa.googlegroups.com...
> >
> > vc wrote:
> >> A union '00' = '00'.
> >
> > This can't be.
> >
> > A union '00' = '00'
> >
> > implies 00 < A, and the partial order "<" being the same in upper and
> > lower semilattice implies that
> >
> > A join '00' = A
> >
> > which we saw isn't.
> >
>
> OK, apparently your definition of '00' is different from mine. What
> relation does '00' stand for ?
Informally, 00 is a relation with 0 attributes and 0 rows. Apparently, it's not easy to define it in lattice terms.
There is another argument against
A union 00 = 00
For any two relations A and B, the relation
A union B
has cardinality bigger than both A and B. In you proposition this
property is lost.