```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:>>>>>>>>>> > On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 21 Mrz., 14:29, William Hughes <wpihug...@gmail.com> wrote:>> > > > On Mar 21, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:>> > > > > > > In fact? That's amazing. So we cannot prove that all lines of the> > > > > > > infinite set of lines are unnecessary?>> > > > > > 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.>> > > > > 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>> > > > Yes, removed one at a time>> > > > >such that no  member remains>> > > > nope, working one at a time you will not get> > > > to the point that no member remains.>> > > 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.->> 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 thelist.However, you are talking about removing  morethan one line, i,e. a *set* of lines.  If you want toremove all of the lines you have to remove the set of alllines that are indexed by a natural number.
```