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Topic: VIRGIL CANNOT ANTI-DIAGONALISE THIS POWERSET(N)! <<<<<
Replies: 5   Last Post: Dec 30, 2012 2:10 AM

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 INFINITY POWER Posts: 117 Registered: 11/1/11
Re: VIRGIL CAN ANTI-DIAGONALISE ANY POWERSET(N)! <<<<<
Posted: Dec 29, 2012 11:04 PM

On Dec 30, 1:46 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>
> 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

Date Subject Author
12/29/12 camgirls@hush.com
12/29/12 Virgil
12/29/12 INFINITY POWER
12/30/12 Virgil
12/30/12 INFINITY POWER
12/30/12 Virgil