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Re: THE FOUNDATION OF NUMBERS BY CANTOR!
Posted:
Jun 2, 2012 4:31 AM
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On Jun 2, 6:12 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
> 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.
>
1+1+1+1... is S(S(S(...S(0)...)))
= |N| = countable infinity
You're the nitwits who defined 2X2X2X2X.. as something bigger.
Just ANSWER MY QUESTION..
the infinite novels.
Actually ADDRESS THE ACTUAL QUESTION...
Herc
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