Date: Dec 6, 2012 5:21 PM
Author: netzweltler
Subject: Re: Matheology § 170
On 4 Dez., 07:48, WM <mueck...@rz.fh-augsburg.de> wrote:

> Matheology § 170

>

> The infinite triangle formed by the sequence

>

> 0.1

> 0.11

> 0.111

> ...

>

> has height aleph_0 but width less than aleph_0 (because the limit 1/9,

> the first line with aleph_0 digits, does not belong to the triangle).

> This lack of symmetry is disturbing for a physicist.

>

> But it would be completely unclear, what side of the infinite triangle

> is the first one to complete infinity aleph_0, when constructed in the

> following manner:

>

> a

>

> a

> bb

>

> c

> ac

> bbc

>

> d

> dc

> dac

> dbbc

>

> d

> dc

> dac

> dbbc

> eeeee

>

> ...

>

> Regards, WM

There is a similar problem. If we construct this infinite list in

countably many steps:

00

01

000

001

010

011

100

101

110

111

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

...

we cannot tell how the infinite list looks like. It could be the list

of natural numbers { ...0000, ...0001, ...0010, ... }, or it could be

the list of the binary complement of the natural numbers { ...1111, ...

1110, ...1101, ... }. Even if the resulting infinite lists are

completely different - the finite lists during construction are

exactly the same for each step in both cases.

--

netzweltler