Re: Proposal: 6NF

Cimode wrote:
> dawn wrote:
> > Cimode wrote:
> > > dawn wrote:
> > >
> > >
> > > > Again, that depends on your definition of NULL. I don't understand how
> > > > you would not think it depends on your definition. Do you think these
> > > > letters fell from the sky with a meaning attached?
> > > Values are universally defined as output of functions and NO science
> > > does not fall from the sky...
> > >
> > > > Not convinced? I dare you to produce/define ANY function that certainly
> > > > produces NULL as an output. If you can't then just shut the hell
> > > > up...and stop confusing people...
> > >
> > > > I did produce one. If you would like to see it in action, you can use
> > > > the open source dbms OpenQM. Remember, this is NOT an SQL NULL.
> > > > OpenQM does not support SQL.
> > > Stating that f(NULL) = NULL is NOT a proof and F(x) = x NOT a precise
> > > example of a function...cos(x) is an example of function 2(x) + 3 is a
> > > function... Do you know what is a function?
> >
> > I am quite sure that produced a valid function. There are three
> > values in the domain of my function, "M", "F" and NULL (Yes, in this
> > case it is a value and no, it is not an SQL NULL, but it is a NULL
> > none-the-less). If you are looking for a function on an interval
> > domain on the real numbers, then we could define a function g on the
> > intervale [0,1] where
> >
> > f(0) = "Male"
> > f(1) = "Female"
> > f(x) = NULL for all x in the interval (0,1)
> >
> > This, too, is a function, even if not a function mapping reals to
> > reals. NULL is not, of course, a real number, even if it is a
> > legitimate output value for a function whose domain is the real numbers
> > or a subset thereof.
> How practical? redefining functions to fit your definition...
> What is the god damn formal expression of function F? One do not
> define functions on intervals...For F(X) X represents ALL values of the
> domain (inputs) from which F extracts ..not just the one that fit your
> faulty conclusions...

OK, Cimode -- What is your definition of "function"? Is there some resource on the web that defines "function" your way? I'm using what I know to be a valid mathematical definition of a function. I believe it also aligns with one in the cdt glossary. We are going to go around in circles if you have a definition of a function that differs with this.

> > > You did not demonstrate anything except that you don't understand
> the
> > > formal mathematical definition of a function...
> >
> > If someone will confirm that you are correct in this, I will revisit
> > what I have though to be the definition of a function. I suspect,
> > however, that you are the one who needs to revisit the definition and
> > verify that I have presented you now with two functions where NULL is a
> > value in the range of the function.
> What you have presented is NOT a mathematical function
>
> http://en.wikipedia.org/wiki/Function_(mathematics)
> //In mathematics, a function relates each of its inputs to exactly one
> output. A standard notation for the output of the function f with the
> input x is f(x). The set of all inputs that a function accepts is
> called the domain of the function.//

OK, so you do have an acceptable description of a function, so what are you not understanding? Are you thinking that functions that do not have the domain and codomain (set from which the range values come) as the set of real numbers are not functions? My first function can be represented as f(x) where x is an element of {"M","F",NULL} while the second can be represented as f(x) where x is an element of the interval [0,1]. I could produce one whose domain is all real numbers if that would suit your fancy, but the domain would not be all real numbers, because you were looking for a function where the output could be NULL.  NULL is represented mathematically as {} (not in SQL, of course, where it is not a value, but an indicator for the lack of a value}.

So, I think you need to understand sets that are not simply from and to the real numbers. This is not intended to be a jab, but you really could start with the exercises we give pre-schoolers where there is a set of animals they then map to the sounds they make, or a set of hats which map to people in professions who wear those hats. Get back to the definition of a function so that you really grok it, then see if you understand what I am writing. Each element in the domain of the function maps to one and only one element in the codomain.

Here is a valid function from {"John", "George", "Paul", "Ringo"} to a codomain of the real numbers. f(x) = 1963

That means that f("John") = 1963 as does f("Paul")

Can you see that we can define a function f(x) where x is an element of the above set and instead of f(x) = 1963 and instead of the codomain being the real numbers, the codomain could be the set containing a single element, the null set. Codomain is { {} }

f(x) = {} for all x in the beatles set above. This is a valid function.

Many developers work with a data/language combination where a NULL value is treated mathematically as the empty set.

> > > You consider as logical
> > > *proof* a specific example of implementation (open source bulshit)...
> >
> > Nope, that was not the logical proof -- the function was. In case you
> > were confused, I suggested you could give it a whirl in an open source
> > dbms.
> That is not a god damn function...A function is not defined throught
> intervals...

Again, you must have such a different perspective of what a function is than what I have learned (and taught) that we will get no where until you a) provide your definition and preferably also b) you learn the standard mathematical definition.

> [nonsense snipped]
>
> > Sometimes confused, but in this case not so much. smiles. --dawn
> Only idiots smile at their ignorance...

Or completely misread the smiles of others? --dawn Received on Sun Oct 08 2006 - 15:51:06 CEST