Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 263
Posted: May 17, 2013 2:56 AM

In article
Graham Cooper <grahamcooper7@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.
> >
> >
> >

> > > All your answers are wrong!
> >
> > 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.
--

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