In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 16 Nov., 22:40, Uirgil <uir...@uirgil.ur> wrote: > > In article > > <24e2d593-d2fc-4163-96f0-7f812a47f...@l18g2000vbv.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > 1. WM Profil anzeigen bersetzen in die Sprache: > > > Deutsch bersetzt (Original anzeigen) > > > Weitere Optionen 16 Nov., 10:35 > > > > > Newsgroups: sci.logic, sci.math > > > Von: WM <mueck...@rz.fh-augsburg.de> > > > Datum: Fri, 16 Nov 2012 01:35:48 -0800 (PST) > > > Lokal: Fr. 16 Nov. 2012 10:35 > > > Betreff: Matheology 152 > > > Antworten | Antwort an Autor | Weiterleiten | Drucken | Einzelne > > > Nachricht | Original anzeigen | Entfernen | Diese Nachricht melden | > > > Nachrichten dieses Autors suchen > > > Matheology 152 > > > > > Consider the following sequence of decimal numbers, consisting of > > > digits 0 and 1 > > > > > 01. > > > 0.1 > > > 010.1 > > > 01.01 > > > 0101.01 > > > 010.101 > > > 01010.101 > > > 0101.0101 > > > ... > > > > > which, when indexed by natural numbers, yilooks like this: > > > > > 0_2 1_1 . > > > 0_2 . 1_1 > > > 0_4 1_3 0_2 . 1_1 > > > 0_4 1_3 . 0_2 1_1 > > > 0_6 1_5 0_4 1_3 . 0_2 1_1 > > > 0_6 1_5 0_4 . 1_3 0_2 1_1 > > > 0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1 > > > 0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1 > > > ... > > > > > What is the limit of the sequence of the sets of indexes on the left > > > hand side? > > > What is the limit of the decimal numbers? > > > > First, you need to show, formally, that those sequences actually have > > limits. > > No. Every mathematician knows that the sequence of numbers grows > without limit.
While every real mathematician knows that SOME sequences grow without limits, they also know that others don't, something that WM seems not to know, which puts him in his place..
> This can be proved by taking any numbr n and showing > that there is a number k such that all for terms a(j) of the sequence > with k > j we have a(j) > n. Proof: For given n take k = n + 10.
ow does that work for the sequence a(j) = 0 for all j? > > Every set theorist knows that the sequence of sets of indices left of > the decimal point has the limit empty set. This is an requirement of > set theory.
Then let us see which axiom, or set of axioms, of some set theory which actually requires such nonsense. say among the axioms for ZFC, for example. > > And finally everybody knows that decimal numbers, by definition, > cannot consist of digits that have no indexs.
Numbers (decimal or otherwise) can exist without any digits of any sort, but decimal numerals can not.
Since a numeral is merely a name for a number, and not actually the thing named, treating numerals as if they were numbers is the sort of error that only putzers like WM are prone to making.