Re: Proposal: 6NF

On Oct 19, 6:42 pm, "vc" <boston..._at_hotmail.com> wrote:
> 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.

As far as I understood from my school years, an operation just mapped one set of values to another. I remain unconvinced of the need for an operation upon a set to map to itself. Where is such a definition? As I said, I am open to convincing, but I was not aware of such a pre-requisite for closure? Received on Fri Oct 20 2006 - 00:51:00 CEST