Re: Proposal: 6NF
Date: Tue, 17 Oct 2006 03:04:58 GMT
Message-ID: <uLXYg.3570$IW6.1566_at_trndny01>
"dawn" <dawnwolthuis_at_gmail.com> wrote in message
news:1161016610.873974.21850_at_h48g2000cwc.googlegroups.com...
> 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.
> >
> > When one says "the set of integers", one usually refers to a set of
> > things possessing some properties, addition/multiplication/subtraction
> > operations obeying certain laws.
>
> 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.
>> > excludes one or more operations, then one makes the mistake of
> > If one says "the set of integers" and
> > 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
>
Agree with dawn. When I first learned set theory, they used the words
"group" and "field" to describe
a set with one or two operators defined on it. The word "set" does not,
AFAIK, imply any operations.
With one possible exception. The elements of a set have identity.
Otherwise you can't distinguish them.
The operator "identify x" (whatever that means) has to be defined over all
sets.
Received on Tue Oct 17 2006 - 05:04:58 CEST