Re: Function

vldm10 wrote:

> 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.

Another difference I see with Jan's is a sense of direction.

How about this:
cdt glossary proposal:

>> [Codomain]
>> See function, math context.
>>
>> [Domain]
>> 1. Given a relation R, a domain is a set Sn such
>> that for each tuple (A1, A2, ...An, ...Am) in R,
>> An is an element of Sn.
>>
>> 2. A domain is a set of values: for example
>> "integers between 0 and 255",
>> "character strings less than 10 characters long",
>> "dates".
>> Sometimes used synonymously with type.
>>
>> 3. Domain of a function. See function, math context.
>>
>>
>>
>> [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:
>>
>> 1. General
>> A purpose or use.
>>
>> 2. Math
>> A binary mathematical relation over two sets D and C that
>> associates with each element in D exactly one element in C.
>> Set D is called the domain of the function, C its codomain.
>>
>> 3. Software
>> A subroutine, procedure, or method.
>>
>>
>> In both the math and software context, there is a sense of
>> direction from domain (input) to codomain (output).
>> For most purposes, this intuitive picture is good enough:
>>
>> |------------|
>> --- x ---- >| f-machine |------ f(x) ----- >
>> |------------|
>>
>> Where x is input in the "f-machine" and f(x) is output.
>>
>> notes:
>> every operator is a function
>> every function is a relation

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