Re: Infinity and indefinite extensibility

"-CELKO-" <jcelko212_at_earthlink.net> wrote in message news:1148150575.564720.155650_at_j55g2000cwa.googlegroups.com...
> >> There is probably some standard terminolgy for what you are about to
read.<<
>
> Most of it comes from Cantor and set theory. Before Cantor, infinite
> was a process and hence the "tipped over" 8 notation. It is the
> programmer's endless loop written with a symbol to show there is no
> upper bound. This is why you see it in limits and summation of a
> series.
>
> After Cantor, we got the aleph notation. The numbers are put into a
> set and the set is treated as a completed whole thing and not a process
> -- the SQL model. It gets a bit tricky when you do summation over a
> set instead of looping over a sequence.

Aleph is notation, not terminology. I think explaining sets of transfinite cardinality in terms of SQL comes dangerously close to begging the question about whether infinite domains can be manipulated in a finite state machine.

>
> If you have a test for set membership that meets certain conditions,
> then you do not need to mateiralize the whole set.
>

Now we're getting somewhere. The question I have is whether the representation of an infinite domain in a finite set of conditions is sufficiently formal to permit one to operate on infinite domains in a finite state machine. Received on Sun May 21 2006 - 23:19:11 CEST