Date: Dec 30, 2012 12:50 AM
Author: Virgil
Subject: Re: VIRGIL CAN ANTI-DIAGONALISE ANY POWERSET(N)! <<<<<
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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