Re: RM and definition of relations/tuples

Martin Zapf wrote:
> vc wrote:
> > Martin Zapf wrote:
> >
> >>I have a question to the Relational Model and the definition of
> >>relations and tuples.
> >>
> >>
> >>I learned the following definitions:
> >>
> >>A relation schema R is a set of Attributes R={A_1,A_2,...,A_n}
> >>Each Attribute A has a domain dom(A)
> >>
> >>Here comes the problem, there are two definitions for relations/tuples
> >>
> >>1. defintion:
> >>
> >> A relation r for schema R is a mathematical relation (cartesian
> >> product) over the
> >> domains from the attributes of R.
> >> So r:=dom(A_1)xdom(A_2)x...xdom(A_n)
> >> A tuple is an element of r.
> >>
> >>2. definition
> >>
> >> A relation r for schem R is a set of tuples.
> >> A tuple t is a function
> >> t: R -> Union (dom(A_1),dom(A_2),...,dom(A_1))
> >> t maps each Attribute of R to an value of its domain.
> >> So a relation is a set of functions, which are called tuples.
> >>
> >>
> >>I noticed, that the difference between this two definition is that
> >>definition 1 forces a certain order for the Attributes and the values
> >>for them in the tuples.
> >>The 2. definition doesnt need any order for the attributes.
> >>
> >>
> >>Im quite confussed, is there a "better" definition or should you always
> >>use both?
> >
> >
> > The first definition is closer to the "mathematical" relation where a
> > tuple is an *ordered* sequence. The second definition is what database
> > folks prefer to use (see Codd, Date, et al) where a tuple is a *set* of
> > attribbute:value pairs. One can be mapped to the other and I would not
> > worry too much about the difference unless you are doing some d.b.
> > theoretical research.
> >
>
> I also figured that out, a mathematical relations (subset of catesian
> product) is ordered because the elements of a cartesian products are
> ordered sets by definition.

The tuples (attributes) are ordered, the elements of the relation (tuples) are not.

> And yes I have to do some theoretical db stuff so Im asking myself:
> If there are two definitions for the same thing, what is the universal
> valid and precise definition for the RM? This two definitions cant come
> out of nowhere, can they.

You might want to search cdt for the glossary as both a mathematical and database version of the definition are there. I chose those after doing some research to find something that could be generally agreed upon. Date has a rather extensive definition that is much more complex than either of these. We had some discussions about his definition a while back too on cdt.

If you have problems finding useful information in the archives, let me know. Also, if you have a definition of relation that you prefer to work with, I'm interested in that too.

Thanks. --dawn Received on Mon Nov 28 2005 - 15:11:32 CET