Re: Relational lattice
From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Tue, 15 Mar 2005 19:52:03 GMT
Message-ID: <D1HZd.38493$ue7.3246150_at_phobos.telenet-ops.be>
>>How about small counter example?
>>where
>>
>>X12=
>>
>>x y
>>- -
>>1 2
>>2 2
>>2 3
>>3 3
>>3 2
>>
>>X34=
>>
>>x y
>>- -
>>1 2
>>2 2
>>2 3
>>3 3
>>3 2
>>1 3
>>
>>X56=
>>
>>x y
>>- -
>>1 3
>>
>>is a solution that meets conditions 1-4. (The fact that x5=1 and x6=3
>>is the only pair is especially handy when checking the above
>>conditions).
Date: Tue, 15 Mar 2005 19:52:03 GMT
Message-ID: <D1HZd.38493$ue7.3246150_at_phobos.telenet-ops.be>
Vadim Tropashko wrote:
> Vadim Tropashko wrote: >
>>How about small counter example?
Oh, that would be splendid. :-)
>>Consider
>>
>>R=
>>
>>x y
>>- -
>>1 2
>>2 2
>>2 3
>>3 3
>>
>>I suggest that
>>
>>X = X12 join X34 join X56
> > > "join" here is merely a Cartesian Product. (ASCII constraint: Can't use > "x" for the product as it can be confused with the variable. "*" sign > for the cartesian product is goofy.) > >
>>where
>>
>>X12=
>>
>>x y
>>- -
> > > typo: > > x1 x2 > -- -- > >
>>1 2
>>2 2
>>2 3
>>3 3
>>3 2
>>
>>X34=
>>
>>x y
>>- -
> > > typo: > > x3 x4 > -- -- > >
>>1 2
>>2 2
>>2 3
>>3 3
>>3 2
>>1 3
>>
>>X56=
>>
>>x y
>>- -
> > > typo: > > x5 x6 > -- -- > >
>>1 3
>>
>>is a solution that meets conditions 1-4. (The fact that x5=1 and x6=3
>>is the only pair is especially handy when checking the above
>>conditions).
Hmm, your relation doesn't satisfy the second part of condition 2 because X12 <> R.
- Jan Hidders