george
Posts:
800
Registered:
8/5/08
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Re: Simple Refutation of Cantor's Proof
Posted:
Dec 24, 2012 10:26 AM
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On Dec 24, 3:01 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> +----->
> | 0. 542..
> | 0. 983..
> | 0. 143..
> | 0. 543..
> | ...
> v
>
> OK - THINK - don't back explain to me.
>
> You run down the Diagonal 5 8 3 ...
>
> IN YOUR MIND - you change each digit ONE AT A TIME
>
> 0.694...
>
> but this process NEVER STOPS
>
> and you NEVER CONSTRUCT A NEW DIGIT SEQUENCE!
Damn, you're stupid. INFINITY DOES *NOT*HAVE*ANY*thing to do with
this!
If you don't like the infinite part, JUST PRETEND THAT IT'S A LIST OF
7
rational numbers that are only 7 decimal digits wide. Guess what:
There is an 8th one that IS NOT ON the list. The anti-diagonal of a
square
list of digits IS NEVER ON the list. It is also not unique -- you
don't have
to use 9-x to complement the digits -- ANY FUNCTION OF THEM AT ALL
that leaves
none of them the same -- for example, "6 if it's not 6 and 7 if it is
6" -- would
WORK JUST AS WELL. THIS PROVES THERE ARE TONS AND TONS of numbers NOT
ON your list
(if it's square). THAT IS ALL that is going on and the question of
"completion"
or infinity IS NOT relevant -- the theorem ALSO holds true for FINITE
lists because
it holds for ALL square lists, PERIOD.
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