Re: Function

On Jan 14, 4:56 pm, 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).
>  > Software
>  > A subroutine, procedure, or method.
>  >
>  > notes:
>  > every operator is a function
>  > every function is a relation
>  >
>  > Please be specific.
>
> --
> What you see depends on where you stand.

I think it will be good to have two definitions for the functions in your glossary.
Definition1 A function from A to B is a rule that assigns, to each member of set A, exactly one member of set B.

And second definition is similar to Jan's suggestion, but slightly changed:
Definition2
A function from A to B is a relation between A and B that associates each element of A with exactly one element of B.

First definition says that a function do something. You can call it intutive definition of a function. Here the function in fact is a procedure as you mentioned.
Second definition is set theoretic. Received on Tue Jan 15 2008 - 06:40:17 CET