Date: Dec 29, 2012 6:40 PM
Author: Virgil
Subject: Re: Should LOGIC PROGRAMMERS worry about SETS BIGGER THAN INFINITY?

In article 
<bfe7c687-cd4a-4ae7-843d-e87587143227@d2g2000pbd.googlegroups.com>,
Graham Cooper <grahamcooper7@gmail.com> wrote:

> ALL OF SCI.MATH A RESOUNDING - 'YES'
>
> and 100 MEGABYTE of USELESS PROOFS TO GO WITH IT
>
> and GET CALLED A KRANK IF YOU POST AN ALTERNATIVE!
>
>
>
>
> 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
>
>
> OK NOW YOU WANT TO ISOLATE
> THAT PATH THROUGH T
>
> AND ONLY THAT PATH THROUGH T!
>
> ***************************************
>
> 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.
--