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.