Turing Compliant?
Travis Oliphant
olipt at mayo.edu
Mon Sep 6 21:05:12 EDT 1999
> On 6 Sep 1999 23:22:23 GMT, Aahz Maruch wrote:
> >Charles G Waldman <cgw at fnal.gov> wrote:
> >>jhefferon at my-deja.com writes:
>
> >>> Not infinite. Unbounded.
>
> >>I'd be interested to hear what the difference is, according to you,
> >>between "infinite" and "unbounded". According to me, they are the
> >>same thing. "finite"=="bounded" => !finite==!bounded.
>
> >Consider the real numbers in the range 0.0 through 1.0. They are
> >bounded but infinite.
>
> ...but he's speaking of memory, an item which has to be enumerated in
> order to be measured. Thus, unbounded memory is infinite memory.
>
> Oh, and for an equally technical nit-pick: contrary to your claim, none of
> the numbers in the range between 0.0 and 1.0 are infinite. The
> cardinality of the set, OTOH, is infinite and unbounded.
We won't even bring up that the cardinality of this set is even larger
than the simply unbounded enumerable sets.
I suppose I shouldn't go there but the infinitity of infinities is a
concept that has always enchanted me.
Travis
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