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Re: Matheology § 203
Posted:
Jan 31, 2013 4:23 AM
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On 31 Jan., 10:04, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 31, 9:48 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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>
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> > On 30 Jan., 22:38, William Hughes <wpihug...@gmail.com> wrote:
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> > > On Jan 30, 10:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > On 30 Jan., 22:14, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > On Jan 30, 6:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > On 30 Jan., 12:32, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > On Jan 30, 12:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > > On 30 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > > Summary. We have agreed that
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> > > > > > > > > For a potentially infinite list L, the
> > > > > > > > > antidiagonal of L is not a line of L.
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> > > > > > > Do you agree with the statement
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> > > > > > > For a potentially infinite list, L,
> > > > > > > of potentially infinite 0/1 sequences
> > > > > > > the antidiagonal of L is not a line
> > > > > > > of L
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> > > > > > Yes, of course. We have a collection of which we can keep a general
> > > > > > overview. And in finite sets (potential infinity is nothing but finity
> > > > > > without an upper threshold) "for every" means the same as "for all".
> > > > > > There is no place to hide.
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> > > > > So now we have
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> > > > > For a potentially infinite list, L,
> > > > > of potentially infinite 0/1 sequences
> > > > > the antidiagonal of L is not a line
> > > > > of L
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> > > > > Can a potentially infinite list, L,
> > > > > of potentially infinite 0/1 sequences
> > > > > have the property that every
> > > > > potentially infinite 0/1 sequence
> > > > > is a line of L?
>
> > > > Potential infinity is the opposite of completeness like "infinite" is
> > > > the opposite of "finished". So *every* line number n would not imply
> > > > *all* possible line numbers of the set |N defined by AxInf.
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> > > This does not answer the question. Please answer the question.-
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> > The question is not properly defined.
> > Do you mean "every" in the potential sense of "all from 1 to n"? Or do
> > you mean "every" in the sense of "all" of set theory?
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> > The latter is wrong, the former is correct.
> > (Note also every potentially infinite sequence only consist of finite
> > initial segments.)
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> Let L be the potentially infinite
> list of natural numbers
>
> 1
> 2
> 3
> ...
>
> Does L have the property that
> every (in the sense of "all from 1 to n")
> natural number is a line of L
>
Yes.
Regards, WM
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