Re: Orlow cardinality question

Alan Morgan said:
> In article <MPG.1cfd33c7fe861cd989cf5@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >Robert Kolker said:
> >> Tony Orlow (aeo6) wrote:
> >>
> >> >
> >> > I found some of the discussion with Phil. There seems to be the same issue
> >> > being discussed regarding the impossible infinite set of finite naturals.
> >>
> >> What is impossible about it. Any element of the set you want can be
> >> arrived at by applying the correct number of of successions to the first
> >> integers.
> >>
> >> Bob Kolker
> >>
> >Can you get an infinite number of integers without an infinite number of
> >successions? No. If you perform an infinite number of successions and
> >increments, do you still have all finite values? No. So, any infinite set of
> >naturals necessarily contains elements with infinite values,
>
> Let's consider, for the moment, the set of finite integers. We will ignore
> people who claim that all integers are finite and consider just the subset
> (perhaps proper, perhaps not) of them that definitely are. As I see it,
> there are three possibilities
>
> 1. The set of finite integers is finite
> 2. The set of finite integers is infinite
> 3. The set of finite integers is ill-defined and thus doesn't have to
> be finite, infinite, or exist at all.
>
> Which you do believe is true?
>
> Alan
>
3. It's ill defined, as there is no upper bound. I was using the word
"indeterminate". It seems people spend a lot of time talking about how you
can't count from the finite to the infinite or vice versa, and how there's not
greatest finite. All that says to me is that counting doesn't work for bridging
that gap. It doesn't seem like something worth putting too much emphasis on.
What appears flat and endless on a local scale turns out to be a little blue
ball, once you're in orbit. The number line looks locally straight but is an
infinite circle. And, taking finite steps makes achieving infinite an infinite
process.
--
Smiles,

Tony
.

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