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From: David BL <davidbl@iinet.net.au>
Newsgroups: comp.databases.theory
Subject: Re: Is a function a relation?
Date: Tue, 30 Jun 2009 02:28:24 -0700 (PDT)
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On Jun 30, 4:49 pm, Cimode <cim...@hotmail.com> wrote:
> On 30 juin, 03:51, David BL <davi...@iinet.net.au> wrote:> On Jun 29, 11:01 pm, Cimode <cim...@hotmail.com> wrote:
>
> > > <<
> > > Given a relation type (i.e. schema), there are a number (possibly
> > > infinite) of relation values that conform to that type.  The type and
> > > the values of that type are all abstract and carry almost no
> > > information. >>
> > > The cardinality of un-ary relation subtype can *not* exceed the
> > > cardinality of the relation supertype.  That is a constraint imposed
> > > by how a relation is defined.
>
> > Sure. Why did you say that?
>
> Just a word of caution over the term *infinite*.

ISTM that in practise all types of interest to computer software must
either be finite or countably infinite.  For example a domain type
that consists of all the finite strings is countably infinite but
nevertheless a reasonable idealisation for real computers (i.e.
despite the potential for running out of memory).

By contrast, uncountably infinite sets are generally useless in
computer science because the elements can't be encoded in a
satisfactory manner. Consider for example sets of infinite strings, or
the power set over the integers.