# Re: A Simple Notation

From: David Cressey <cressey73_at_verizon.net>
Date: Sat, 07 Jul 2007 15:55:03 GMT
Message-ID: <rHOji.255\$qu5.189_at_trndny02>

"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.
>

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.

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