> In article > <firstname.lastname@example.org>, > WM <email@example.com> 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 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.
-- Neueste Forschungsergebnisse aus deutschen Spitzenhochschulen. Heute von Prof. Dr. Wolfgang Mückenheim, Mathematikkoryphäe der FH Augsburg, aus seiner Postille "Physical constraints of numbers": "Even some single numbers smaller than 2^10^100 ... do not exist."