Date: Nov 16, 2012 8:34 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 152

On 16 Nov., 13:58, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 16, 5:46 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > 1.  WM    Profil anzeigen   Übersetzen in die Sprache:
> > DeutschÜbersetzt (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
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> > 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?

>
> A set.


The empty set.
>
> > What is the limit of the decimal numbers?
>
> A value.


Not a value, but infinity, i.e., the infinite of analysis: potential
infinity, a continuous growth.

And we see the poor numbers, which must hold the position on the left
hand side of the decimal point, existing without indices which have
been stripped off. But what is a digit of a decimal number without its
index? Shouldn't we call such numbers crippled numbers? Or is
"mathematically challenged" the correct wording?

Regards, WM