# Re: Proposal: 6NF

From: JOG <jog_at_cs.nott.ac.uk>
Date: 19 Oct 2006 09:44:23 -0700

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}.

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>
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> 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]

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. Received on Thu Oct 19 2006 - 18:44:23 CEST

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