Re: Proposal: 6NF

JOG wrote:
> 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.

>

f:SxS -> S is not "a set to map to itself". We are talking here about very very basic stuff that's known if not from the primary school then at least from the secondary school agebra (or at least should be).

>Where is such a definition? As I

If books are not read any more nowadays, then this might help:

http://mathworld.wolfram.com/BinaryOperation.html Received on Fri Oct 20 2006 - 02:02:47 CEST