Virgil
Posts:
8,833
Registered:
1/6/11


Re: VIRGIL CAN ANTIDIAGONALISE ANY POWERSET(N)! <<<<<
Posted:
Dec 30, 2012 12:50 AM


In article <kboeg7$s7e$1@dontemail.me>, "INFINITY POWER" <infinity@limited.com> wrote:
> On Dec 30, 1:46 pm, Virgil <vir...@ligriv.com> wrote: > > In article > > <49449aa441e24c5bb12032cfcc328...@px4g2000pbc.googlegroups.com>, > > > > camgi...@hush.com wrote: > > > USE YOUR ANTIDIAGONAL 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. 

