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Topic: The Diagonal Argument
Replies: 28   Last Post: Dec 29, 2012 12:11 AM

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Graham Cooper

Posts: 4,262
Registered: 5/20/10
Re: The Diagonal Argument
Posted: Dec 26, 2012 2:43 PM
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On Dec 26, 6:47 pm, George Greene <gree...@email.unc.edu> wrote:
> On Dec 26, 12:28 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>

> > it fails because with Infinite Sets of Reals
> > You can alter the Number Order
> > To change the digit back!

>
> THAT DOESN'T CHANGE anything!
> You can permute the list of reals ANY WAY YOU LIKE.
> That will give you A DIFFERENT anti-diagonal and thus a DIFFERENT new
> number
> but NEITHER THE NEW ANTI-DIAGONAL NOR THE OLD ONE will be on EITHER
> list!
> Obviously permuting the list does NOT change the answer to ANY
> question of the
> form "is x on this list?".  It might change WHERE it is, if it's on
> there,
> but it does NOT change the answer to "yes it is" or "no it isn't".
>

> > Its like putting a coin on a 2UP paddle
> > and giving it a one way opposing flip.

>
> > Null Operation as you just flip it twice!
>
> That's just ONE DIGIT, DUMBASS. THE ISSUE is about THE WHOLE
> new anti-diagonal.  Changing the list does NOT change ANY digits of
> the OLD
> ORIGINAL anti-diagonal.  It gives you a NEW list with a NEW anti-
> diagonal.
> Which is ALSO NOT ON the list.
> The issue in any case IS NOT EVEN WHETHER "the argument fails".
> The issue is whether the anti-diagonal IS OR IS NOT ON the list.
> And it is OBVIOUSLY NOT ON IT since it differs from EVERY real on the
> list.
>


Try to Visualise an example.

L(x,y)
+---------------->
| 0. 2 3 4 5 6 7 ..
| 0. 9 8 7 6 5 5 ..
| 0. 1 2 3 1 2 3 ..
| 0. 9 8 9 8 9 8 ..
| 0. 6 5 6 5 6 5 ..
| 0. 5 6 5 6 5 6 ..
|
v

Now apply your FLIP(d) function to the whole plane

T(x,y)
+---------------->
| 0. 6 6 6 6 5 5 ..
| 0. 5 5 5 5 6 6 ..
| 0. 6 6 6 6 6 6 ..
| 0. 5 5 5 5 5 5 ..
| 0. 5 6 5 6 5 6 ..
| 0. 6 5 6 5 6 5 ..
|
v


Your claim is that is you take any path from

T(1,?)
T(2,?)
T(3,?)
...

and repeat that process you must end up with an infinite string absent
from L?

Totally Wrong!

I put T(1,?) onto the 2UP Paddle (5 or 6 my choice) and you Flip
It Over!



Herc




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