Date: Dec 29, 2012 11:04 PM
Author: INFINITY POWER
Subject: Re: VIRGIL CAN ANTI-DIAGONALISE ANY POWERSET(N)!  <<<<<

On Dec 30, 1:46 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <49449aa4-41e2-4c5b-b120-32cfcc328...@px4g2000pbc.googlegroups.com>,
> 
>  camgi...@hush.com wrote:
> > USE YOUR ANTI-DIAGONAL METHOD
> > ON THIS SET OF *ALL* SUBSETS OF N!
> 
> NO! I see no evidence of any surjection from any set to its power set

I said N.


> 
>  S       P(S)
> ---     ------
> {}       {{}}  No bijection
> {a}      {{a},{}} No bijection
> {a,b}    {{a,b}, {a}, {b}, {}}
> 

That has nothing to do with the Powerset.

For any FINITE SET you can create a larger set just by adding 1 element.




1 <=>  {1,3,4,5...} 
2 <=>  {1,2,3,4,5,6,7,8,9,10...} 
3 <=>  {1} 
4 <=>  {2,4,6,8,10,...} 
..

Virgil Fails to show any missing subset of N

FORMULA  (semi-decidable)

x e PS(N)_ss <->  TM_ss(x) halts



Herc