Re: Proposal: 6NF
Date: 19 Oct 2006 10:42:44 -0700
Message-ID: <1161279763.908861.23820_at_h48g2000cwc.googlegroups.com>
JOG wrote:
> 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?
It's not a 'closure'. The closure property, in this context, means that the result of a binary operation must belong to the same set the operands come from What are '0' and '1' ? They do not exist in {2, 3}, so {2, 3} is not closed under '+ mod 4'. Very much in the same fashion, the natural numbers are not closed under subtraction, or odd numbers under addition, etc.
> After all, any operation just maps one
> set of values to another - why the self-closure requirement?
Any math binary operation should map pairs of values from some set to a value in the same set (SxS -> S), that's the essential property of the math structures known from one's school years, such as the natural numbers, the set of ntegers, the set of rationals, the set of reals, the complex numbers, etc,
>
> I stand ready for correction if I have made a misinterpretation.
Received on Thu Oct 19 2006 - 19:42:44 CEST