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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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netzweltler

Posts: 304
From: Germany
Registered: 8/6/10
Re: THE FOUNDATION OF NUMBERS BY CANTOR!
Posted: Jun 2, 2012 4:12 AM
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On 1 Jun., 08:40, Graham Cooper <grahamcoop...@gmail.com> wrote:
> 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


Why should 2x2x2x2... be different from 1+1+1+1...? In the first case
it is the same as 2+2+4+8+16+...
In all cases the result is omega.

--
netzweltler



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