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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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Virgil

Posts: 8,833
Registered: 1/6/11
Re: VIRGIL CAN ANTI-DIAGONALISE ANY POWERSET(N)! <<<<<
Posted: Dec 30, 2012 12:50 AM
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In article <kboeg7$s7e$1@dont-email.me>,
"INFINITY POWER" <infinity@limited.com> wrote:

> 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


When you have given me an allegedly complete listing of the subsets of N
I will find a set that you have omitted from your list.

Supposing any list of subsets of N, f(1), f(2), f(3), ..., then
the set S = { x in N: x not in f(x)}, is not included in that list.
--





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