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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 4, 2013 4:48 PM

You can't prove it's not on the list , but you can't prove it is on
the list either (if you could prove it , you would match the number
0.111.... to one of your finite definitions (eg. 0.1111 ) on the
list ).

> Therefore there are no actually infinite sequences at all - and there
> is no Cantor-list, other than finitely defined lists.

False . Either there are only finite-sequence lists with with a finite
number of terms ,
or there are infinite lists with infinite terms .

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

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?

In other words , how come this :

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

is valid
and this :

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

is not valid? What's possible for the columns of a list must be
possible for the rows . The same constraints must apply both to the
indexes of the real numbers in your list (vertical indices) , and to
the indexes of your digits (horizontal indices) .

More specifically : you have a list of (FINITE sequences of digits) .
Your list an INFINITE number of (horizontal FINITE sequences of
digits) :

vertically infinite / horizontally finite .
0
0 1
0 1 1
0 1 1 1
0 1 1 1 1
............
............
............

Why can't my list have a INFINITE number of (vertical FINITE
sequences of digits) ?

vertically finite / horizontally infinite .
0 0 0 0 0 ...
1 1 1 1 ...
1 1 1 ...
1 1 ...
1 ...

The same indexing method for members of a list is used for digits of a
member.
What works for the columns must work for the rows . What works for the
vertical must work for the horizontal .
If you have infinite members you must allow infinite digits in a
member . If you have infinite digits in any member, you must allow
infinite members .

Date Subject Author
4/29/13 Virgil
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4/30/13 dan.ms.chaos@gmail.com
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