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Math Forum » Discussions » sci.math.* » sci.math.independent

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: 108
Registered: 11/1/11
Re: VIRGIL CAN ANTI-DIAGONALISE ANY POWERSET(N)! <<<<<
Posted: Dec 29, 2012 11:04 PM
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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

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