# Re: A Simple Notation

Date: Sat, 07 Jul 2007 14:10:54 -0300
Message-ID: <468fc907\$0\$4314\$9a566e8b_at_news.aliant.net>

David Cressey wrote:
> "paul c" <toledobythesea_at_oohay.ac> wrote in message
> news:skOji.94053\$NV3.69985_at_pd7urf2no...
>

```>>Brian Selzer wrote:
>>
>>>"paul c" <toledobythesea_at_oohay.ac> wrote in message
>>>news:PAAji.92566\$xq1.59731_at_pd7urf1no...
>>>
>>>
>>>>Brian Selzer wrote:
>>>>
>>>>
>>>>>"David Cressey" <cressey73_at_verizon.net> wrote in message
>>>>>news:eirji.2\$475.1_at_trndny04...
>>>>>
>>
>>...
>>
>>>>I wonder when, in the course of the usual human affairs as they involve
>>>>the basic relational dbms op's, does it make sense to think of infinite
>>>>domains?  Isn't it usually sufficient, as far as algebra is concerned,
```

>
> to
>
```>>>>pretend they are finite?
>>>>
>>>
>>>
>>>Why limit yourself to what can be represented in a computer?  An algebra
>>>that supports relations with infinite cardinality or degree can
```

>
> certainly
>
```>>>support any relation that can be represented in a computer.
>>
>>As somebody here said (perhaps it was you, I forget), it seems important
>>to separate relational operators from the rest of a language where we
>>can do non-relational things, such as arithmetic addition.  As far as a
>>dbms that stores extensions/propositions is concerned, I don't see that
>>it is possible to store infinite sets of values, so I wouldn't know how
>>to implement that.
```

>
> I'd like to distinguish, if you'll bear with me, between "infinite" and
> "indefinitely extensible".
>
> With regard to relations themselves, you might want to distinguish between
> relations of finite cardinality and ones of infinite cardinality. (I assume
> that's a countable infinity. Some mathematician can correct me if I'm
> wrong.)
>
> With regard to the scheme by which relations are represented inside a
> computer, a scheme could be "indefinitely extensible" meaning that there
> is no largest relation within the architectural limits of the scheme. Yet,
> at any given point in time, there will be a largest, finite relation that
> has ever been thus represented.
>
> A simple example of an indefinitely extensible scheme (not necessarily a
> good scheme) is null terminated ASCII. There is no largest character string
> that can thus be represented, but the scheme is only good for finite
> strings.
>
> It seems to me that, if you can, it's a good idea to get the underlying
> math to deal with the infinite, to get the representation scheme to at
> least be infinitely extensible, and to let the current implementation
> impose some chosen upper architectural limit.

The infinite poses some easily avoided problems when one realizes one won't ever have to deal with the infinite. Various paradoxes, in particular, become moot. Received on Sat Jul 07 2007 - 19:10:54 CEST

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