Date: Jan 17, 2013 4:07 AM Author: Virgil Subject: Re: WMatheology §Organization: Anon In article <kd89vt$ton$1@news.m-online.net>,

Ralf Bader <bader@nefkom.net> wrote:

> Virgil wrote:

>

> > In article

> > <e0aee8bf-b163-4cad-ab72-a2f200da9913@f19g2000vbv.googlegroups.com>,

> > WM <mueckenh@rz.fh-augsburg.de> wrote:

> >

> >> On 16 Jan., 20:16, Virgil <vir...@ligriv.com> wrote:

> >>

> >> > > > > Your string can and will differ from the nth string. But there

> >> > > > > will always an identical string be in the list

> >> >

> >> > > > Identical to what?

> >> >

> >> > > Identical to every initial segment of the anti-diagonal.

> >> >

> >> > If that alleged "identical string" were in some position n in the list

> >> > then it will differ from any anti-diagonal at its own position n.

> >>

> >> There are infinitely many positions following upon every n. So if your

> >> assertion is true for every n, then there are infinitely many

> >> remaining for which it is not true. This holds for every n.

> >

> > My "assertion" is that for each n in |N, the antidiagonal differs from

> > string n in place n.

> >

> > AS as the antidiagonal differing from a string in one place means that

> > the antidiagonal differs from that string, we have that the antidagonal

> > differs from EVERY string in al least one place per string, which is all

> > that is needed

> >> >

> >> > So there is nowhere in the list that can occur without differing from

> >> > an antidiagoal.

> >>

> >> Tell me the n which allows you to consider your check as completed.

> >

> > What makes you think there is a "last" one, when all of them are done?

>

> You shouldn't underestimate the weirdness of MÃ¼ckenheim's concoctions, and

> also not overestimate the necessity to discuss this nonsense. "Infinite",

> according to MÃ¼ckenheim, probably means "always finite, but continually

> growing beyond any preassigned finite limitation". So, a MÃ¼ckenheimian

> infinite decimal fraction has always a finite number of digits, but there

> are some more the next time you look at it. Then, the decimal expansion of

> 1/9 is still different from any one of the finite exoansions 0,1...1, but

> another feat of MÃ¼ckenheimian genius is to confound the never-ending growth

> process attributed to the expansion of 1/9 with the state it has reached at

> the present moment. And this then does the feat and makes it impossible to

> distinguish 1/9=0,111... from all of its finite approximations. This is

> quite trivial and totally idiotic. But it is in perfect harmony with the

> fraction of MÃ¼ckenheim's Collected Nonsense I happened to read.

>

> That there is a "last" one (for example the latest stage of such a

> potentially infinite process if it ever were completed) probably is a kind

> of imagined-with-the-inner-eye logical necessity for MÃ¼ckenheim. I

> rememeber that as a little child I could not imagine how the sea looks;

> that is, a surface of water stretching to the horizon without an opposite

> shore that always popped up in my imaginations. That problem persisted as

> long as I had been told about the sea but never seen it and vanished in the

> moment I saw a picture of the situation. In a similar way it seems to be

> impossible for MÃ¼ckenheim to grasp something actually (not in the

> always-growing sense) countably infinite without a boundary at the far end.

I am not so much concerned with the exact mature of MÃ¼ckenheims mucking

up logic and mathematics a trying to show innocent others that it is

only mucking up of logic and mathematics.

--