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

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Graham Cooper

Posts: 4,280
Registered: 5/20/10
Re: Matheology § 263
Posted: May 14, 2013 5:18 PM
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On May 15, 5:13 am, Virgil <vir...@ligriv.com> wrote:
> In article
> <5461da31-3edf-4357-a12b-02be4857d...@d8g2000pbe.googlegroups.com>,
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On May 14, 6:43 pm, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <fe808d30-0f12-4c95-8708-3d6053afe...@oy9g2000pbb.googlegroups.com>,
> > > Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > On May 14, 4:46 pm, Virgil <vir...@ligriv.com> wrote:
> > > > > In article
> > > > > <d6f681f1-613b-4e57-a336-5ab501a04...@wb17g2000pbc.googlegroups.com>,
> > > > > Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > > > On May 14, 1:36 pm, Virgil <vir...@ligriv.com> wrote:
> > > > > > > In article
> > > > > > > <d8620fe3-928d-4bc5-bf24-b16bee326...@wb17g2000pbc.googlegroups.com>
> > > > > > > ,
> > > > > > > Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > > > > > On May 14, 11:09 am, Virgil <vir...@ligriv.com> wrote:
> > > > > > > > > In article
> > > > > > > > > <4f6cc18e-90b2-415e-83aa-963e1c083...@n5g2000pbg.googlegroups.co
> > > > > > > > > m>,
> > > > > > > > > Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > > > > > > > such as Virgil's favorite number!
>
> > > > > > > > > > 0.44444454444444444445444444545544444444445444444444444...
>
> > > > > > > > > That denotes, as yet, any of a range of real numbers, not any
> > > > > > > > > specific
> > > > > > > > > one, and whichever ones in that range Graham finds his
> > > > > > > > > favorite,
> > > > > > > > > none of
> > > > > > > > > them are anything like my favorite.

>
> > > > > > > > Real numbers of that form are all you need to show
>
> > > > > > > I don't need to show any any such numbers.
>
> > > > > > > > | POINTS | > | INFINITE LIST |
>
> > > > > > > > between these 2 bars!
>
> > > > > > > > --->|----|<----
>
> > > > > > > > Here's another one
>
> > > > > > > > 0.4444444444445444444444454444445444444444454444445444444...
>
> > > > > > > > Remember your hero CANTOR showed you how to CONSTRUCT that
> > > > > > > > number!

>
> > > > > > > > You post 20 times a day the Algorithm (sic) to construct that
> > > > > > > > real!

>
> > > > > > > The algorithm I regularly post, and Cantor first used, is for
> > > > > > > binary
> > > > > > > sequences not decimals.

>
> > > > > > > Neither type of "antidiagonal" is defined without an infinite list
> > > > > > > of
> > > > > > > sequences of the the appropriate type from which to build it, which
> > > > > > > lists you have not provided, so no anti-diagonal need exist until
> > > > > > > you
> > > > > > > do.

>
> > > > > > Such algorithms have been posted 100 times.
>
> > > > > > Though You have no clue what Cantor's Missing Set function actually
> > > > > > does.

>
> > > > > > SET1 = { 1 , 3 , 6 }
> > > > > > SET2 = { 1 , 5 , 11 }
> > > > > > SET3 = { 2 , 4 , 6, 8 , 10 , ... }
> > > > > > SET4 = { 4 , 5, 6, 7, 8 }

>
> > > > > > [VIRGIL]
>
> > > > > > Given an arbitrary function f from |N to the powerset of |N (set of
> > > > > > all subsets of |N), the set S = {n in |N | ~ n in f(n)} is a subset
> > > > > > of
> > > > > > |N not in the image of f, and thus is a proper "Cantor's missing
> > > > > > set".

>
> > > > > > You learnt this magic formula off by heart and you have no idea how
> > > > > > to
> > > > > > apply it!

>
> > > > > I have learnt the quadratic formula off by heart, too, though, at need
> > > > > I
> > > > > can derive it from the quadratic equation, a*x^2 + b*x + c = 0, and
> > > > > apply it.

>
> > > > > > and the Missing Set from the above enumeration is.... ?
>
> > > > > In order to be able to use the definition "S = {n in |N | ~ n in f(n)}"
> > > > > and thus determine which sets are missing in the image of a given
> > > > > function, f: |N --> 2^|N, one must first be able to determine all the
> > > > > values of that function, i.e., one subset of |N for each member of |N..

>
> > > > > If you only give me
>
> > > > > f(1) = { 1 , 3 , 6 }
> > > > > f(2) = { 1 , 5 , 11 }
> > > > > f(3) = { 2 , 4 , 6, 8 , 10 , ... }
> > > > > f(4) = { 4 , 5, 6, 7, 8 }

>
> > > > > All I know so far is that that your f cannot be such a function
> > > > > because 1 is in f(1) and 4 is in f(4).

>
> > > > <BZZZT!>
>
> > > > Wrong! Try again, what about 2? Is that in your missing set ?
>
> > > Depends on whether f(2) = { 1 , 5 , 11 } or not.
>
> > > If f(2) = { 1 , 5 , 11 } and f(3) = { 2 , 4 , 6, 8 , 10 , ... }
> > > then 2 and 3 will be in that set, S, but that leaves all infinitely many
> > > n in |N with n > 4 still undetermined as to membership in S where
> > > "S = {n in |N | ~ n in f(n)}"

>
> > So you can't calculate any members of C.M.S. given this then?
>
> >  SET1 = { 1 , 3 , 6 }
> >  SET2 = { 1 , 5 , 11 }
> >  SET3 = { 2 , 4 , 6, 8 , 10 , ... }
> >  SET4 = { 4 , 5, 6, 7, 8 }

>


So the Above is a Sequence of ALL SUBSETS OF N

and you admit you have no recourse to prove otherwise!

Thank you for your resignation on this issue!

Herc



Date Subject Author
5/10/13
Read Re: Matheology � 263
Virgil
5/13/13
Read Re: Matheology � 263
Virgil
5/13/13
Read Re: Matheology § 263
Graham Cooper
5/13/13
Read Re: Matheology � 263
Virgil
5/13/13
Read Re: Matheology § 263
Graham Cooper
5/13/13
Read Re: Matheology � 263
Virgil
5/14/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology � 263
Virgil
5/14/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology � 263
Virgil
5/14/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology � 263
Virgil
5/14/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology � 263
Virgil
5/14/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology � 263
Virgil
5/15/13
Read Re: Matheology § 263
Graham Cooper
5/15/13
Read Re: Matheology � 263
Virgil
5/15/13
Read Re: Matheology § 263
Graham Cooper
5/15/13
Read Re: Matheology � 263
Virgil
5/15/13
Read Re: Matheology § 263
Graham Cooper
5/15/13
Read Re: Matheology � 263
Virgil
5/15/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Scott Berg
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology � 263
Virgil
5/16/13
Read Re: Matheology § 263
Graham Cooper
5/17/13
Read Re: Matheology � 263
Virgil
5/17/13
Read Re: Matheology § 263
Graham Cooper
5/17/13
Read Re: Matheology � 263
Virgil
5/17/13
Read Re: Matheology § 263
Graham Cooper
5/17/13
Read Re: Matheology � 263
Virgil
5/17/13
Read Re: Matheology § 263
Graham Cooper
5/17/13
Read Re: Matheology � 263
Virgil
5/17/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology § 263
Graham Cooper
5/14/13
Read Re: Matheology � 263
Virgil

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