Date: Mar 22, 2013 3:30 AM
Author: William Hughes
Subject: Re: Matheology § 224

On Mar 22, 7:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 21 Mrz., 16:41, William Hughes <wpihug...@gmail.com> wrote:
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> > On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 21 Mrz., 14:29, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Mar 21, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > In fact? That's amazing. So we cannot prove that all lines of the
> > > > > > > infinite set of lines are unnecessary?

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> > > > > > We can prove that something is true for every
> > > > > > member of an infinite set. We cannot
> > > > > > prove that something is true for the set
> > > > > > itself unless the set is finite.

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> > > > > But I am not interested in the set itself. Not at all! My claim is
> > > > > that every member of the set of lines can be removed

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> > > > Yes, removed one at a time
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> > > > >such that no  member remains
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> > > > nope, working one at a time you will not get
> > > > to the point that no member remains.

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> > > Induction does not need time.
> > > The conclusion from n on n+1, if valid, is valid for every natural at
> > > one instance.

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> > Yes, valid for every natural, but not valid
> > for the *set* of all naturals.-

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> I do not talk about this *set* when removing lines. My proof shows
> that every line can be removed from the list without removing any
> natural number from the list.


No your proof shows that *any* *one* line can be removed from the
list.
However, you are talking about removing more
than one line, i,e. a *set* of lines. If you want to
remove all of the lines you have to remove the set of all
lines that are indexed by a natural number.