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Topic: THE FOUNDATION OF NUMBERS BY CANTOR!
Replies: 6   Last Post: Jun 2, 2012 4:33 PM

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Graham Cooper

Posts: 4,237
Registered: 5/20/10
Re: THE FOUNDATION OF NUMBERS BY CANTOR!
Posted: Jun 1, 2012 2:40 AM
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On Jun 1, 4:07 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
> On 31 Mai, 05:38, Graham Cooper <grahamcoop...@gmail.com> wrote:
>

> > THE FOUNDATION OF NUMBERS BY CANTOR!
>
> > AD[r]=/=LIST[r,r] -> AD[r]=/=LIST[r,r]
>
> > -> 2^aleph_0 > aleph_0
>
> > -> 2x2x2x2... > 1+1+1+1...
>
> > Incomplete..Inconsistent..Uncomputable..Uncountable..Unformalizable..
> > Unspecifiable..NotUniversal..NotVerifiable

>
> > Gee  I  W o n d e r  why that is!!??
>
> > Herc
>
> As far as I know 2 x 2 x 2 x ... actually means the infinite cartesian
> product {0,1} x {0,1} x {0,1} x ...
> If you calculate this product step by step (in countably infinitely
> many steps) you will NOT get the set of all infinite binary sequences.
> As you can see here (intermediate results of the calculations shifted
> to the right):
>
> Step 1:
>
> ...00000 0
> ...00000 1
> ...000010
> ...000011
> ...000100
> ...000101
> ...000110
> ...000111
> ...001000
> ...
>
> Step 2:
>
> ...0000 00
> ...0000 01
> ...0000 10
> ...0000 11
> ...000100
> ...000101
> ...000110
> ...000111
> ...001000
> ...
>
> Step 3:
>
> ...000 000
> ...000 001
> ...000 010
> ...000 011
> ...000 100
> ...000 101
> ...000 110
> ...000 111
> ...001000
> ...
>
> and so on, you simply get the infinite binary sequences of the natural
> numbers (if ...000001 = 001 = 01 = 1).
>



If the infinite sequence of Universal Turing Machines (emulated from 1
starting UTM)

can permute the calculations equivalent to
<TM1, TM2, TM3, TM4,...>

in all possible computable permutations of N

1X2X3X4X5X6...

then the amount of binary sequences, only

2X2X2X2X2X2...

should fit inside that list easily!



Herc



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