In article
<3cd5d88d-8e43-44f5-b121-a0ee775287fe@[EMAIL PROTECTED]
>,
Marshall <marshall.spight@[EMAIL PROTECTED]
> wrote:
> On Jan 22, 11:48 am, Paul Rubin <http://phr...@[EMAIL
PROTECTED]
> wrote:
> >
> > Set theory doesn't figure into it anywhere as far as I know.
>
> That seems a bit extreme to me. Set theory IMHO is always worth
> a good look. And certainly if the programming language being
> discussed is say, SETL or SQL, then set theory is very relevant.
>
>
> > Anything having to do with programming
> > language theory is (as far as I can tell) entirely about the
> > countable.
>
> Funny, I was pondering this very issue earlier today.
> I don't think it is strictly true. Certainly our languages,
> and what they can compute, are only countably infinite,
> but we ought not limit our attention to the countable,
> if only to understand exactly where lies the line between
> what is and is not computable. And we may also consider
> that we often find ourselves writing programs that need
> to approximate the behavior of real arithmetic. The domain
> of our approximation may be finite but the domain being
> approximated (the reals) in uncountable.
Maybe. You can also view it that the domain being approximated is the
*constructible* reals, which are countable. Most of the useful facts of
real analysis carry over to the constructible reals (e.g. Bishop's work
with Intuitionism), so the common practice of considering the underlying
domain to be the full reals is plausibly more of a historical artefact
than a necessity.
> Marshall
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