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

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 263
Posted: May 14, 2013 10:21 PM
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In article
<6fb0173e-8640-476e-9875-c3230cdbc331@g5g2000pbp.googlegroups.com>,
Graham Cooper <grahamcooper7@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".
--




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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