```Date: Nov 17, 2012 3:12 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 152

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 growswithout limit. This can be proved by taking any numbr n and showingthat there is a number k such that all for terms a(j) of the sequencewith k > j we have a(j) > n. Proof: For given n take k = n + 10.Every set theorist knows that the sequence of sets of indices left ofthe decimal point has the limit empty set. This is an requirement ofset theory.And finally everybody knows that decimal numbers, by definition,cannot consist of digits that have no indexs.Regards, WM
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