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Re: Should LOGIC PROGRAMMERS worry about SETS BIGGER THAN INFINITY?
Posted:
Dec 30, 2012 1:54 AM
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"Virgil" wrote in message >
> 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
>
> FLIP(d) = 6 IFF d<6
> FLIP(d) = 5 OTHERWISE
>
>
> Now apply your FLIP(d) function to the ENTIRE LIST
>
> 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
>
> T(x,y)
> +---------------->
> | 0. 6 X X X X X ..
> | 0. X 5 X X X X ..
> | 0. X X 6 X X X ..
> | 0. X X X 5 X X ..
> | 0. X X X X 5 X ..
> | 0. X X X X X 5 ..
> | ..
> v
>
> ***************************************
>
> PERMUTING THE LIST
> AND TAKING THE ANTI-DIAGONAL
>
> IS *EQUIVALENT* TO
>
> SELECTING A PATH THROUGH
> THE TRANSPOSE LIST
>
>****************************************
EVERY "path" taking one AND ONLY ONE element from each row and column of
the T'd list and no two elements from any row or any column of the T'd
List will NOT be in the unT'd list.
So you have found at least countably many nonmembers of the original
list.
>
> ***************************************
>
> SAME THING!
>
> YET THERE IS NO MISSING REAL
> WHEN YOU DO IT MY WAY!
Curious, then, that there are so many of them for those who know how to
look for them.
***********HERC************
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
Here's a few more:
0.656555...
T(x,y)
+---------------->
| 0. 6 X X X X X ..
| 0. X 5 X X X X ..
| 0. X X 6 X X X ..
| 0. X X X 5 X X ..
| 0. X X X X 5 X ..
| 0. X X X X X 5 ..
| ..
v
0.566555...
T(x,y)
+---------------->
| 0. X 6 X X X X ..
| 0. 5 X X X X X ..
| 0. X X 6 X X X ..
| 0. X X X 5 X X ..
| 0. X X X X 5 X ..
| 0. X X X X X 5 ..
| ..
v
0.665555...
T(x,y)
+---------------->
| 0. X 6 X X X X ..
| 0. X X 5 X X X ..
| 0. 6 X X X X X ..
| 0. X X X 5 X X ..
| 0. X X X X 5 X ..
| 0. X X X X X 5 ..
| ..
v
0.666556...
T(x,y)
+---------------->
| 0. X 6 X X X X ..
| 0. X X X X X 6 ..
| 0. 6 X X X X X ..
| 0. X X X 5 X X ..
| 0. X X X X 5 X ..
| 0. X X 6 X X X ..
| ..
v
Does that like MORE THAN INFINITY to you Virgil?
Herc
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