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Re: Matheology § 203
Posted:
Jan 30, 2013 3:28 AM
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On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote:
>
> <snip>
>
> > > It does, however, imply that d in not one
> > > of the lines of the list L
>
> > For that sake you must check all lines. Can you check what is not
> > existing?
>
> So now your claim is
>
> We can know
>
> There does not exist a natural number n
> such that d is equal to the nth line
> of L
>
> but we cannot know
>
> d is not one of the lines of L
You are trying hard to misunderstand!
For a potentially infinite set L we can know: d is not in line number
n.
But a potentially infinite set is not actually infinite. And without
actually infinite sets, you have no uncountability. For instance, all
finite subsets of |N make up a countable power set. Only the actually
infinite subsets make up an uncountable power set. But "actually
infinite" means a number larger than every n. It is easy to understand
that this number can never be exhausted by finite numbers n. Therefore
we cannot prove that d is missing in the actually infinity list from
"for every n in |N, there is no line n that contains d".
We will never know something for all lines as we will never be able to
know all lines, since beyond every line n there are infinitely many
following.
Regards, WM
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