Re: Function

On 14 jan, 22:56, mAsterdam <mAster..._at_vrijdag.org> wrote:
> vldm10 wrote:
>
>  > David Cressey wrote: >> vldm10 wrote:
>
>  >>>> David BL wrote:
>  >>>>> This however doesn't change the fact that most authors
>  >>>>> define a (mathematical) relation as a set
>  >>>>> of ordered tuples, which means a function is not a relation
>  >>>>> (assuming, as most do, that a function has
>  >>>>> a defined domain and codomain).
>  >>>> I don't understand how the conclusion follow from the premise.
>  >>> I am afraid that you don't understand above conclusion
>  >>>  because you don't understand what function is.
>  >> What makes you think that?
>  >
>  > Definition1    A function from A to B is a rule that assigns,
>  > to each member of set A, exactly one member of set B.
>  >
>  > Is this good or bad definition for a function?
>  > If you thing that this is good definition for a function then
>  > please explain why this is good definition,
>  > else please explain why it is not good definition.
>  > Your answer on my question will be also answer on your question.
>
> This is getting silly. Did you even read the question?
>
> How did you assess David's lack of understanding 'function'?
> What gave you that impression?
>
> This is not the first time that 'function' popped up as pivotal
> to some misunderstandings in cdt - but I fail to see where
> the unclarity is right now.
>
> (cdt glossary:)
>
>  > [Function]
>  > For now we have to live with different meanings
>  > of _function_ when talking about databases:
>  > "The function of this function is to get the tuples from B
>  > that are functionally dependant on A."
>  >
>  > Three different contexts, but just about the same meaning:
>  >
>  > General
>  > A purpose or use.
>  > Math
>  > A binary mathematical relation with at most
>  > one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe! Moreover, it seems to describe partial functions, which is not what is usually understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates with each element in D exactly one element in C."

You might even add something about calling D and C domain and codomain respectively, although that might open up a whole new can of worms.

Of course, I'm still convinced that the c.d.t. glossary is a waste of time, but there you go. ;-)

• Jan Hidders