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> The consequence of admitting the premice that a relation is a specific
> subset of functions is that you apply all characteritics of a function:
> Funny. For some reason I thought that in math, the functions were
a
> subset of the relations. And therefore, the relations are a
superset
> of the functions. It hurts to discover one's own ignorance.
I have to admit I have struggled with that concept a few years but I came to the conclusion that relations were indeed a subset and not a superset of function as you are stating.
Think about it...
For a an ensemblist mathematical set to be declared a subset of an other ensemblist mathematical set it must first inherit ALL characteritics of the superset...In short,
IF set1 INCLUDE set2
then set2 (caracteristics on elements of set2) = set1(caracteristics on
elements of set2) + set2(caracteristics on elements of set2)
An application for instance of the above is between rationals and integers
Integers are a subset of Rationals because they inherit all characteristics common to ALL Rationals. but have characteristics of their own....
You can have for instance the following hierarchy
RATIONALS I INTEGER DECIMAL
If I follow your reasoning and based on the above. If you state that a function is a subset of relation then you must admit that a function ANY function share the characteristics of relation.....Let's see one characteristic of relations: multidimensionality. ARE ALL functions multidimensional? linear functions are not multidimensional.
OTOH, if you consider the opposite, meaning relations as a subset of functions then you realize the definition applies correctly...For instance, functions use variables to represent dynamic value place holders. You will realize that characteristics applies to all functions whether relations, linear etc.....One could represent it as follows...
FUNCTIONS RELATIONS LINEAR TRIGO. Etc...
But you seem convinced of the opposite...Thanks for demonstrating logically your point B4 stating anything. LIstenning.
> > --> relations, relvars, relvalues are on different level of definition.
>
> Do I understand you correctly that by "relvalue" you mean "any possible
> value from any possible domain that can occur within a relation" ? You
> have already pointed out that, acoording to Codd, each defined relation
> establishes a new domain of its own. I take it that the values of such
> a domain are indeed "relation values". It would then follow, if I
> understand you correctly, that all relation values are "relvalues" but
> not all "relvalues" are relation values.
Not quite...Relations are higher level concept than relvar. One Domain
defined at relation level is not the same as a domain from which
values are drawn at attribute data type level. The relationship
between the two is a complex relationship to define (for instance how
operators apply between attribute data type and operator which apply to
the relation as a data type)
Does it make better sense.
> Then I think that what you mean by "relvalue" is just "value".
You are correct.
I personally prefer *value* but some people brought the issue of
*relvalue* in a pedagogical. Some of the people stated that relation
= relvar = relvalue which as you seem to understand is not quite the
same.
> > --> R-tables are ONE possible representation of relvars.
>
> Sorry. R-tables are one possible representation of RELATION VALUES.
You are correct. This definition may lead to confusion. Instead, I
should have stated
"R-Tables are a projection or representation of relvars in a specific point in time"
which is basically equivalent to
...You are also correct asserting that they represent values rather than variables. I tend to look at it in a time perspective..I consider that values are *variable fillers* in time.
Thank you for bringing that out.
> Variables simply do not *need* "being represented". They have a name,
> a declared type, and they contain a value. Date models variables as a
> triple of exactly these three components.
Represented seems to be a non consensual term. Projected seems to be a
better term.
Nevertherless, I am curious about your statement...Do you consider that
relvar do not need to be projected...In that case, how do you operate
them?
> > Hope this clarified.
>
> I wouldn't bet on it.
Received on Mon Jun 19 2006 - 05:58:05 CDT