Re: Function
From: Kira Yamato <kirakun_at_earthlink.net>
Date: Tue, 15 Jan 2008 14:14:45 -0500
Message-ID: <2008011514144516807-kirakun_at_earthlinknet>
>>>>> [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.
Date: Tue, 15 Jan 2008 14:14:45 -0500
Message-ID: <2008011514144516807-kirakun_at_earthlinknet>
On 2008-01-15 11:29:40 -0500, mAsterdam <mAsterdam_at_vrijdag.org> said:
> Kira Yamato schreef: >> mAsterdam said: >> >>> vldm10 wrote: >>>> [...] >>> 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.
>> >> This is not good enough. > > Could you provide a better text?
A domain is simply a set of values.
> >> It is possible that a value exists in the domain Sn yet the relation >> has no corresponding tuple which holds that value for An. > > Does the current text forbid that?
In your original definition, you require a tuple in R that holds that value in order for that value to be in Sn.
I'm saying that this requirement is not needed.
>
>>>>> 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.
>> >> This seems right. A domain is just a set of values. In relational >> algebra, this set is required to be non-empty since attributes are >> non-null. > > It is worm season, it seems :-)
Yea. Some relational algebra textbooks make a big case of why attributes should not be null.
>
>>>>> 3. Domain of a function. See function, math context.
>> >> On the other hand, mathematics does not require a domain to be non-empty. >>
>>>>>
>>>>>
>>>>>
>>>>> [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."
>> >> No, there is always just one meaning of function in database. > > Would s/meanings/uses/ take away your objection? > If not, which one meaning?
Perhaps s/meanings/definition/ is better.
>
>>>>> 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.
>> >> Essentially correct, although to be rigorous you need to define how >> such binary relation can define the meaning of "associating each >> element in D exactly one element in C." >> >> Not all binary relation has this property. > > IMHO this goes way beyond the glossaries purpose. > However, if you have a simple replacement that would cover this it > would be welcome.
It is over the top for practical uses. I was just being pedantic. :)
> [...]
-- -kiraReceived on Tue Jan 15 2008 - 20:14:45 CET