Date: Jan 17, 2013 4:07 AM
Author: Virgil
Subject: Re: WMatheology §Organization: Anon

In article <kd89vt$ton$>,
Ralf Bader <> wrote:

> Virgil wrote:

> > In article
> > <>,
> > WM <> wrote:
> >

> >> On 16 Jan., 20:16, Virgil <> 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 Mückenheim's concoctions, and
> also not overestimate the necessity to discuss this nonsense. "Infinite",
> according to Mückenheim, probably means "always finite, but continually
> growing beyond any preassigned finite limitation". So, a Mückenheimian
> 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 Mückenheimian 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 Mückenheim'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 Mückenheim. 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 Mückenheim 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 Mückenheims mucking
up logic and mathematics a trying to show innocent others that it is
only mucking up of logic and mathematics.