# Re: Function

Date: Tue, 15 Jan 2008 15:26:01 +0100

Message-ID: <478cc147$0$85781$e4fe514c_at_news.xs4all.nl>

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
*

-- What you see depends on where you stand.Received on Tue Jan 15 2008 - 15:26:01 CET