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From: "JOG" <jog@cs.nott.ac.uk>
Newsgroups: comp.databases.theory
Subject: Re: Proposal: 6NF
Date: 19 Oct 2006 09:44:23 -0700
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vc wrote:
> Jan Hidders wrote:
> > vc wrote:
> > > Jan Hidders wrote:
> > > [...]
> > >
> > > A much simpler example.  Let {0, 1, 2, 3} be a set of four integers
> > > with addition modulo 4.  Then,  none of its subsets,  except {0} and
> > > {0, 2},  retains the addition mod 4 operation which makes the idea of
> > > 'subtype as subset' utterly silly, [....].
> >
> > You keep on making the same mistake. The expression a +[mod 4] b has a
> > well defined result if a and b are from any subset of {0, 1, 2, 3}.
>
>
> Consider the subset {2, 3}.  What is the result of    (2+3) mod 4 ?  If
> you say it's '1', what is '1'?  There is no such element in {2, 3}.
> [snip]

Hi vc. PMFJI, but does this argument not rely on the assumption of  the
set needing to satisfy the closure property in respect to the
operation?

Mathematically, surely the modulo addition operation as described above
above can be applied to the subset {2, 3}, while happily having a
closure of {0,1,2} for instance? After all, any operation just maps one
set of values to another - why the self-closure requirement?

I stand ready for correction if I have made a misinterpretation.