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Topic: Matheology � 263
Replies: 57   Last Post: May 17, 2013 8:52 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Matheology § 263
Posted: May 17, 2013 2:14 AM

On May 17, 4:08 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>

> > On May 17, 11:51 am, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > On May 17, 10:57 am, Virgil <vir...@ligriv.com> wrote:
> > > > > > OK, use
>
> > > > > > f(1) = { 1 , 3 , 6 }
> > > > > > f(2) = { 1 , 5 , 11 }
> > > > > > f(3) = { 2 , 4 , 6, 8 , 10 , ... }
> > > > > > f(4) = { 4 , 5, 6, 7, 8 }

>
> > > > > > f(n) = N | n>4
>
> > > > > > What is set S?
>
> > > > > Note that there are only 5 subsets of N that ARE in the image of your
> > > > > 'f' out of uncountably many subsets of |N to chose from that will be
> > > > > S's, i.e., subset of |N but not values of f.

>
> > > > > They are
> > > > > every finite subset of |N having
> > > > > less that 3 members
> > > > > or exactly 4 members,
> > > > > or more than 5 members,
> > > > > or containing either 2, or a natural larger than 8,
> > > > > and every infinite subset of |N other than f(3) and |N.

>
> > > > > Take your pick.
>
> > > `
>
> > So Cantor's Method does not work?
>
> Since there are far more sets not in the image of any function from |N
> to 2^|N  than in its image, why are you so hot to get one in particular?
>
>
>

> > Your method (white box inspection) does not work for every possible f,
> > as such it is of no consequence.

>
> Name one it does not work for!
>
>
>

> > GIVEN A SPECIFIC f, WHAT IS CANTORS MISSING SET?
>
> If you could pick a subset of |N at random, it would almost certainly
> not be in the image of any randomly chosen function.
>
>
>

>
> They are not in the image of the function you presented, which is all
> they are asked to be.
>

NO! THIS is the question.

f(1) = { 1 , 3 , 6 }
f(2) = { 1 , 5 , 11 }
f(3) = { 2 , 4 , 6, 8 , 10 , ... }
f(4) = { 4 , 5, 6, 7, 8 }

f(n) = N | n>4

What is set S?

from 1 function f() you get 1 set S

You can post *piffle* AFTER you've

CALCULATED_CANTORS_MISSING_SET

Herc

Date Subject Author
5/10/13 Virgil
5/13/13 Virgil
5/13/13 Graham Cooper
5/13/13 Virgil
5/13/13 Graham Cooper
5/13/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Scott Berg
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Virgil
5/16/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/14/13 Graham Cooper
5/14/13 Virgil