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

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Graham Cooper

Posts: 4,237
Registered: 5/20/10
Re: Matheology § 263
Posted: May 15, 2013 3:00 AM
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On May 15, 12:21 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <6fb0173e-8640-476e-9875-c3230cdbc...@g5g2000pbp.googlegroups.com>,
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On May 15, 8:35 am, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <f5fcc9ab-019c-42ac-a18f-9fb28b41d...@ul7g2000pbc.googlegroups.com>,
> > >  Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > 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.googlegro
> > > > > > > > > > > ups.
> > > > > > > > > > > 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.googleg
> > > > > > > > > > > > > roup
> > > > > > > > > > > > > s.co
> > > > > > > > > > > > > m>,
> > > > > > > > > > > > > Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > > > > > > > > > > > such as Virgil's favorite number!
>
> > > > > > > > > > > > > > 0.4444445444444444444544444454554444444444544444444444
> > > > > > > > > > > > > > 4...

>
> > > > > > > > > > > > > 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
>
> > > Are you claiming that |N has only 4 sug=bsets?
>
> > > But you are wrong, since no mere SEQUENCE of sets can contain all
> > > subsets of |N.

>
> > > Any such sequence would, in effect, be a function, say f,  from |N to
> > > 2^|N, the power set of |N, and any such function, f, will never have as
> > > a value the set { n in |N : ~ n in f(n)}

>
> > > Consider any f : {1} --> {{},{1}}
> > > Consider any f : {1,2} --> {{},{1},{2},{1,2}}
> > > Consider any f : {1,2,3} --> {{},{1},{2},{3},{1,2},{1,3},(2,3}.{1,2,3}}
> > > ...
> > > None of those functions can be surjections, and they ever further from
> > > surjection as the sizes of the domains increase, so why expect expect
> > > any change in the limit?

>
> > because you are using a simple powerset function that has no bearing
> > on an infinite domain.

>
> Why not? The difference in sizes between a finite set and its finite
> powerset increases rapidly with the size of the set so what prevents
> the same in the limit?
>

> > because infinite sets of subsets have different properties to finite
> > sets of subsets

>
> How different and why does that difference suggest that the actual limit
> behavior is not actual?
>

> > because your algorithm (sic) never terminates
>
> Infinite sequences which never terminate can still have limits.
>

> > because your algorithm (sic) uses extra information to the set (the
> > particular permutation given)

>
> Nonsense! The size of a powerset depends only on the cardinality of the
> base set, the number of its members, not at all on which particular
> objects are its members. All sets of the same size (are bijectable) have
> powersets of the same size.
>
>
>
>
>
>
>
>
>

> > ....
>
> > GIVEN A LIST OF SUBSETS OF N
>
> > you admit you cannot calculate ANY members of a supposed missing set.
>
> > f(1) = { 1 , 3 , 6 }
> > f(2) = { 1 , 5 , 11 }
> > f(3) = { 2 , 4 , 6, 8 , 10 , ... }
> > f(4) = { 4 , 5, 6, 7, 8 }

>
> > IS 2 e MISSINGSET ?
>
> > Last time asking.
>
> Yes! As previously answered 2 is a member of at least one such missing
> set. And so is 3, at least for one such missing set.
> But there are more sets missing than not missing and 2 need not be
> missing from each of those "missing sets".
>



So Missing Set = { ......... } ????


Can you calculate a missing set or not?


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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