Date: Mar 21, 2013 11:41 AM
Author: William Hughes
Subject: Re: Matheology § 224

On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> 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.


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