Re: Proposal: 6NF

vc wrote:
> Jan Hidders wrote:
> > vc wrote:
> > > Jan Hidders wrote:
> > > > vc wrote:
> > > [...]
> > > > > The most familiar to the OOP person expectation of what the type is is
> > > > > based on the LSP where one can substitute objects of type S for objects
> > > > > of type T, S being a subtype of T, without change in behavior.
> > > > > Clearly, treating Z as subtype of R does not conform the LSP, because
> > > > > Z is not a subfield of R.
> > > >
> > > > Depends on what you think of as the thing that is being defined. Is it
> > > > the algebraic structure or is it the set over which the operations are
> > > > defined? In the first case you cannot treat the Z algebraic structure
> > > > as a subtype of the R algebraic structure, but in the second case you
> > > > clearly can.
> > >
> > > Hold on.
> >
> > Ok. I'm holding on.
> >
> > > o The set plus some operations over the the set *is* an algebraic
> > > structure so there is no substantial difference between case one and
> > > case two. Once again, this is an example of imprecise language which
> > > one would want to avoid (saying 'set' and meaning 'structure').
> >
> > When I say "the set of integers" I mean "the set of integers" and not
> > "the set of integers plus some operations" which is a tuple and not a
> > set.

>

In case another voice would be helpful, if someone says group or ring of integers, for example, then I figure there are operations included, but when someone says "set" then it is a set, with no implication of operators, even if I have some awareness of various possible operators.

If you refer to your set of integers as Z, however, my first inclination is that you mean the ring of integers (set plus + and * operations), but I don't know if that is a solid convention or due to a flawed memory.

> If one says "the set of integers" and
> excludes one or more operations, then one makes the mistake of
> misnaming the structure one is talking about.

Disagree. By calling it a set, you are not hauling any operators on the elements of the set into the description, except perhaps in very casual conversation (I think you mentioned grade school). Just my two cents, in case it is helpful. --dawn Received on Mon Oct 16 2006 - 18:36:50 CEST