# Re: Function

Date: Tue, 15 Jan 2008 14:14:45 -0500

On 2008-01-15 11:29:40 -0500, mAsterdam <mAsterdam_at_vrijdag.org> said:

```> Kira Yamato schreef:
>> mAsterdam said:
>>
>>> vldm10 wrote:
>>>> [...]
>>> 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. :)

> [...]

```--

-kira
```
Received on Tue Jan 15 2008 - 20:14:45 CET

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