Re: Basic question?What 's the key if there 's no FD(Functional Dependencies)?

Brian Selzer wrote:
> "NENASHI, Tegiri" <tnmail42_at_gmail.com> wrote in message
> news:1162516551.190354.4820_at_b28g2000cwb.googlegroups.com...
> > Brian Selzer wrote:
> >> "vldm10" <vldm10_at_yahoo.com> wrote in message
> >> news:1162403098.627006.128180_at_i42g2000cwa.googlegroups.com...
> >> > saturnlee_at_yahoo.com wrote:
> >> >> What 's the key for it? ABC or nothing???
> >> >
> >> >
> >> > ABC is not the key.
> >> > Example: Let one partricular entity has A,B,C atributes
> >> > and let these atributes take the following values:
> >> >
> >> > A B C
> >> > -----------------------------
> >> > 2 4 6
> >> > 8 4 6
> >> > 2 4 6
> >> >
> >> > ( ABC can be the key only in the trivial cases i.e if an entity has
> >> > the atributes whose values never change)
> >> >
> >>
> >> The above example is not a relation. A relation is a set of tuples.
> >> Because it is a set, there can be no duplicates.
> >>
> >> A relation does not contain entities: it contains statements about
> >> entities.
> >
> > I thought in mathematica relation is subset of the product of two or
> > more sets. Or you mean 'relation' from first order logic ? It not
> > contains statements in logic also, its just a formula. Please explain.
> >
>
> No, a relation is a subset of the product of zero or more sets.

No in matemartica relation is a subset of two or more sets.

>You can
> have a relation with zero attributes.

 In relational theory DAte says that it can be zero but I think its not very usable.

>You can have a relation with one
> attribute.

Yes relation with one attribute becomes a set:

{(1,2),(3,3)} -project first-> {1,3}

>RM relations, though similar, are not the same as mathematical

The named values is very old technology. The best is to use the theory of categories for better abstraction and you do not need to name values.

>

In matematica they say that a relation is model of the predicate or formula but relation is not set of statements, no.

> A propositions is a statement
> that is either true or false.

No it's opposite. In logic proposition proposition is statement that can be true or false.

>The point I was trying to make is that a set
> of entities differs from a set of statements about entities.

This is very correct.

There is better thing for database abstraction. Theory of categories is very good for abstraction. Its better than sets because you do not need to think of not important details. Category theory and relational theory is like algebra and multiplication table. Do you want to use algebra or still arithmetic ?

The theory of categories unites object databases, relational database, functional model, NIAM. It replaces theory of sets as fundamental theory also.

--

Tegi

>


> > --

> >

> > Tegi


> >

> >> A key is a subset of the attributes of a relation schema such that the

> >> projection over that subset onto any relation has the same cardinality of

> >> that relation.  A candidate key is a key that exhibits the additional

> >> property that no proper subset of that key is also a key.

> >