In article <email@example.com>, Ralf Bader <firstname.lastname@example.org> wrote:
> Virgil wrote: > > > In article > > <email@example.com>, > > WM <firstname.lastname@example.org> 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. --