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

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 Graham Cooper Posts: 4,422 Registered: 5/20/10
Re: Matheology § 263
Posted: May 17, 2013 6:01 PM

On May 17, 4:56 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > 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
> > > > > <3fb4082c-a455-47a8-a931-c219fd2fb...@qc10g2000pbb.googlegroups.com>,
> > > > > 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
>
> Actually, one has far more sets, S,  not in the image of any such
> function than are in its image.
>
> The smallest is {}, every one element set also works, as does every two
> element set, and all but two of the countably many three element sets.
>
>
>

> > You can post *piffle* AFTER you've
>
> > CALCULATED_CANTORS_MISSING_SET
>
> Cantors does not say that there is no more than one such set, he just
> said that there is at least one, and I have provided at least one, in
> fact uncountably many of them.
>

I want to see the FORMULA

{ n | n ~e f(n) }

WORK ON

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

ALL VALUES OF f() ARE SPECIFIED.

----------

S = { n | n ~e f(n) }

WORK on the GIVEN f ?

If it does - WHAT IS S ?

------------

Not interested in any other missing sets or explanations ABOUT S.

JUST WHAT IS S given that f ?

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