# Re: What to call this operator?

Date: 1 Jul 2005 10:32:09 -0700

Message-ID: <1120239129.850440.157460_at_g44g2000cwa.googlegroups.com>

Jon Heggland wrote:

> In article <1120156799.149832.136240_at_o13g2000cwo.googlegroups.com>,

*> mikharakiri_nospaum_at_yahoo.com says...
**> > > x y <= A
**> > >
**> > > That's right, instead of bracket notation A(x,y) saying that relation A
**> > > has attributes x and y, we can just write "A >= x y" implying that A is
**> > > a superset of join of empty relations x and y.
**> >
**> > On a symmetrical note, lets use capital letters X, Y etc to denote an
**> > infinite relation each of which is a full domain. Then
**> >
**> > A <= X Y
**>
**> Nice, but is it not also so that A >= x y z and A <= X Y Z for A(x,y)?
**> Which makes that notation less useful....
*

A >= x y z transitively follows from

A >= x y x >= x y

However A <= X Y Z doesn't hold. Ascii diagram for the lattice A(x,y) = {(1,a)} with domains X = {1,2} and Y = {a,b} illustrates this assymetry

.....xy .../.|.\ ../..|..\ .x...A...y .|../|\..| .|./.|.\.| .|/..|..\|

{1}..XY.{a}

.|../.\..| .|./...\.| .|/.....\| .X.......Y ..\...../ ...\.../ ....\./ ....{}Received on Fri Jul 01 2005 - 19:32:09 CEST