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Topic: Matheology � 258
Replies: 104   Last Post: May 5, 2013 2:26 PM

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 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: Matheology § 258
Posted: May 5, 2013 6:45 AM

On May 5, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 4 Mai, 22:48, Dan <dan.ms.ch...@gmail.com> wrote:
>

> > You can have a formula for the list , f(a,b) , that gives the b'th
> > digit of the a'th number of the list .
> > You're saying b must be bounded (no infinite sequences of digits)  ,
> > but a can be infinite (an infinite amount of finite sequences) .
> > This is inconsistent . Why should f(a,b) be a valid list but f(b,a) be
> > an invalid list?

>
> A very clear and correct argument!
> Of course there cannot be any asymmetry. This can be proven by the
> obvious bijection between all FIS of the first column and of the
> lines:
>
> 1
> 2, 1
> 3, 2, 1
> ...
>
> But we know from mathematics that a strictly incresing sequence cannot
> contain its limit and also that all natural numbers are finite.
> Therefore all lines are finite. They are potentially infinite, i.e.,
> they are all finite, but you cannot find any threshold, let alone a
> supremum.
>
> Vice versa this implies that the columns, including the first column,
> do not contain their limit. There is no actual infinity, i.e. more
> than every natural number of numbers in the first column.
>
> Regards, WM

The first column is infinite .As is the second. The list
is ,ultimately, just a generalization of the matrix .
And the building blocks of the list aren't potentially infinite or
actually infinite sequences .
The building blocs of the list are finite , bounded digits .
The list is made out of digits (organized in a matrix-like fashion) .
A digit is any member of the set {0,1,2,3,4,5,6,7,8,9} .

This leaves 2 situations :
1) Either you use a finite amount of digits in writing the entire
list :
Eg.

0 1 1
0 1 2 3
0 1 4 4 4

uses exactly 12 digits .

2) Or , you use an infinite amount of digits in writing the entire
list :
Eg.

0.1
0.11
0.111
...

uses an infinity of digits .

If you're going to use an infinity of digits , it doesn't really
matter if you
use up an infinity vertically :

1 1
1 0
1 1
1 0
1 1
1 0
.....

or if you use up an infinity horizontally :

0 1 1 1 1 1 1 1 1 1 1 .....
0 1 0 1 0 1 0 1 0 1 0 ......

or if you use it both ways :

1 0 1 0 1 0 1 0 ....
0 1 0 1 0 1 0 1 ....
1 0 1 0 1 0 1 0 ....
0 1 0 1 0 1 0 1 ....
1 0 1 0 1 0 1 0 ....
0 1 0 1 0 1 0 1 ....
....................
....................

An infinity of digits is still an infinity of digits , no matter how
you choose to spread them throughout the list . That cannot be swept
under the rug .

Date Subject Author
4/29/13 Virgil
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