Re: Matheology § 263

[Virgil]

In article <c4feaff4-1889-4a9f...@googlegroups.com>,
Zeit Geist <tucso...@me.com> wrote:

> On Thursday, May 9, 2013 11:25:15 PM UTC-7, WM wrote:
> > Matheology � 263
> >
> >
> >
> > There are things. They exist by energy (Joule).
> >
> > There are ideas. They exist by information (bit).
> >
>
> I have never seen a Joule or a bit.
> Are sure they exist?
>
> Thought I saw a Newton (unit of force),
> But it was just a cookie with figs in it.
>
> >
> > Regards, WM
>
> ZG

It figures.
--

[Virgil]

In article
<ed22d3cc-e1c2-4506...@b3g2000vbo.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 10 Mai, 11:46, fom <fomJ...@nyms.net> wrote:

> > On 5/10/2013 1:25 AM, WM wrote:
> >
> >
> >
> >
> >
> > > Matheology 263
> >
> > > There are things. They exist by energy (Joule).
> > > There are ideas. They exist by information (bit).
> >

> > > If a plumber asserts to have twenty thousand hammers in his toolbag, I
> > > would carefully supervise his work, if done in in my house.
> >
> > > If a farmer asserts that his barn contains twenty billions potatoes, I
> > > will buy from him expecting very big potatoes. *)
> >
> > > If a mathematician asserts that his model contains uncountably many
> > > indistinguishable but distinct numbers, this will not cause a
> > > sensation.
> >
> > > Isn't that sensational?
> >
> > > *) The joke is based on the German proverb /fortune favours foolish
> > > farmers by increasing the diameter of their potatoes/.
> >
> > > Regards, WM
> >
> > And, seemingly, the platinum bar in Paris increases
> > its length with the apparent passage of time.
>
> Who cares? Never heard that it has retired already 30 years ago?

No one but WM cares about his WMytheology either, which nonsense
certainly should have been retired at least 30 years ago.
--

[Virgil]

In article
<0cd2b58e-96c7-491c...@w13g2000vbn.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 10 Mai, 09:34, Virgil <vir...@ligriv.com> wrote:
>
> >
> > > *) The joke is based on the German proverb /fortune favours foolish
> > > farmers by increasing the diameter of their potatoes/.
> >

> > Fortune does not favor WM
>
> No. Fortune favours fools.

Only in Germany. And there it seems to favor the fool WM by allowing him
to teach his foolishness to others, thus increasing the diameter of WM's
potato, which we call WMytheology.
--

[WM]

On 10 Mai, 21:00, Virgil <vir...@ligriv.com> wrote:
> In article
> <0cd2b58e-96c7-491c-93a5-7c1c6d0ac...@w13g2000vbn.googlegroups.com>,

>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 10 Mai, 09:34, Virgil <vir...@ligriv.com> wrote:
>
> > > > *) The joke is based on the German proverb /fortune favours foolish
> > > > farmers by increasing the diameter of their potatoes/.
>
> > > Fortune does not favor WM
>
> > No. Fortune favours fools.
>
> Only in Germany.

"Fortune favours fools" appeared on several dictionary sites when I
looked for a translation of the German proverb (that you will not
understand when I post it in the original version) into English. Your
ignorance is really universal.

Regards, WM

[Bergholt Stuttley Johnson]

Virgil wrote:
> And there it seems to favor the fool WM by allowing him
> to teach his foolishness to others

Peter Principle

[JT]

Well my advice to WM, fuck the monkeys

[JT]

This is how i see them half cut and fucked up
http://www.youtube.com/watch?v=1SkUxknvRlc

[Virgil]

In article
<297234d9-d2df-4e84...@a3g2000vbr.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 10 Mai, 21:00, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <0cd2b58e-96c7-491c-93a5-7c1c6d0ac...@w13g2000vbn.googlegroups.com>,
> >
> > �WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 10 Mai, 09:34, Virgil <vir...@ligriv.com> wrote:
> >
> > > > > *) The joke is based on the German proverb /fortune favours foolish
> > > > > farmers by increasing the diameter of their potatoes/.
> >
> > > > Fortune does not favor WM
> >
> > > No. Fortune favours fools.
> >
> > Only in Germany.
>
> "Fortune favours fools" appeared on several dictionary sites when I
> looked for a translation of the German proverb

That the language translates does not mean that the effect does.

And those of us not incarcerated in your Wolkenmuekenheim are not
favored by your swelling spuds.
--

[Graham Cooper]

On May 11, 5:00 am, Virgil <vir...@ligriv.com> wrote:
> In article
> <0cd2b58e-96c7-491c-93a5-7c1c6d0ac...@w13g2000vbn.googlegroups.com>,
>

>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 10 Mai, 09:34, Virgil <vir...@ligriv.com> wrote:
>
> > > > *) The joke is based on the German proverb /fortune favours foolish
> > > > farmers by increasing the diameter of their potatoes/.
>
> > > Fortune does not favor WM
>
> > No. Fortune favours fools.
>
> Only in Germany. And there it seems to favor the fool WM by allowing him
> to teach his foolishness to others, thus increasing the diameter of WM's
> potato, which we call WMytheology.
>

WM's potato is not as big as Virgil's favourite number.


0.44444454444444454444454444444554444444454444444444544444..

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

Herc
--

CANTORS POWERSET PROOF

| CARDINALITY | > | INFINITY |

IF SET1 has 1 - then MYSET skips 1
or
IF SET1 skips 1 - then MYSET has 1

AND
IF SET2 has 2 - then MYSET skips 2
or
IF SET2 skips 2 - then MYSET has 2

AND
IF SET3 has 3 - then MYSET skips 3
or
IF SET3 skips 3 - then MYSET has 3

AND
IF SET4 has 4 - then MYSET skips 4
or
IF SET4 skips 4 - then MYSET has 4
...

[Virgil]

"WM" <muec...@rz.fh-augsburg.de> wrote in message
news:5a30a691-8b3d-408e...@m2g2000vbb.googlegroups.com...
>Matheology � 263

.
.

.

>If a farmer asserts that his barn contains twenty billions potatoes, I
>will buy from him expecting very big potatoes.

.
.
.


A mathematically competent person would expect that, unless that barn
covered many hectares and was impossibly tall, each of those twenty
billion potatoes is likely to be remarkably small.

Again evidence of WM's incompetence with anything having to do with
numbers.
--

[Graham Cooper]

On May 14, 6:17 am, Virgil <vir...@ligriv.com> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

such as Virgil's favorite number!

0.44444454444444444445444444545544444444445444444444444...

THAT PROVES YOU NEED MORE THAN I INFINITE LIST | POINTS
to color in the number line!

---->|--------|<-----

Herc

[Virgil]

In article
<4f6cc18e-90b2-415e...@n5g2000pbg.googlegroups.com>,

Graham Cooper <graham...@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.
--

[Graham Cooper]

On May 14, 11:09 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <4f6cc18e-90b2-415e-83aa-963e1c083...@n5g2000pbg.googlegroups.com>,

>  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

| 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!


Herc

[Virgil]

In article
<d8620fe3-928d-4bc5...@wb17g2000pbc.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:

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

[Graham Cooper]

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.com>,
> > > 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!

and the Missing Set from the above enumeration is.... ?


Herc
--
www.BLoCKHeaDs.com

[Graham Cooper]

On May 14, 1:36 pm, Virgil <vir...@ligriv.com> wrote:

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

> The algorithm I regularly post....

<BZZZZT!>

You have no idea what an algorithm is, clearly!


Herc
--
www.BLoCKHeaDS.com

[Virgil]

In article
<b2bf6ead-6c3a-4843...@n5g2000pbg.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:

> On May 14, 1:36�pm, Virgil <vir...@ligriv.com> wrote:
> > > You post 20 times a day the Algorithm (sic) to construct that real!
> >
> > The algorithm I regularly post....
>
> <BZZZZT!>
>
> You have no idea what an algorithm is, clearly!

Cantor's works for me.
>
>
> Herc
> --
> www.BLoCKHeaDS.com
--

[Virgil]

In article
<d6f681f1-613b-4e57...@wb17g2000pbc.googlegroups.com>,

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).
--

[Graham Cooper]

On May 14, 4:46 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <d6f681f1-613b-4e57-a336-5ab501a04...@wb17g2000pbc.googlegroups.com>,

<BZZZT!>

Wrong! Try again, what about 2? Is that in your missing set ?


Herc
--
www.BLoCKPROLOG.com

[Virgil]

In article
<fe808d30-0f12-4c95...@oy9g2000pbb.googlegroups.com>,

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)}"

>
>

> Herc
> --
> www.BLoCKPROLOG.com
--

[Graham Cooper]

On May 14, 6:43 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <fe808d30-0f12-4c95-8708-3d6053afe...@oy9g2000pbb.googlegroups.com>,

So you can't calculate any members of C.M.S. given this then?

[Virgil]

In article
<5461da31-3edf-4357...@d8g2000pbe.googlegroups.com>,

Specification of a particular "Cantor's missing set" or
"S = {n in |N | ~ n in f(n)}", requires first a definition of the
function f from the set of naturals |N to the power set of the set of
naturals usually denoted by P(|N) or 2^|N.

When you, or anyone else , has defined such a function completely,
then I can define a set not in the range of that function.
--

[Graham Cooper]

On May 15, 5:13 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <5461da31-3edf-4357-a12b-02be4857d...@d8g2000pbe.googlegroups.com>,

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

[Virgil]

In article
<f5fcc9ab-019c-42ac...@ul7g2000pbc.googlegroups.com>,

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?
--

[Graham Cooper]

On May 15, 8:35 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <f5fcc9ab-019c-42ac-a18f-9fb28b41d...@ul7g2000pbc.googlegroups.com>,

because you are using a simple powerset function that has no bearing
on an infinite domain.
because infinite sets of subsets have different properties to finite
sets of subsets
because your algorithm (sic) never terminates
because your algorithm (sic) uses extra information to the set (the
particular permutation given)
....



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.

Herc

[Virgil]

In article
<6fb0173e-8640-476e...@g5g2000pbp.googlegroups.com>,

Graham Cooper <graham...@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.

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".
--

[Graham Cooper]

On May 15, 12:21 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <6fb0173e-8640-476e-9875-c3230cdbc...@g5g2000pbp.googlegroups.com>,

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


Can you calculate a missing set or not?


Herc

[Virgil]

In article
<0982dd8e-550d-4f48...@oy9g2000pbb.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:

> On May 15, 12:21�pm, Virgil <vir...@ligriv.com> wrote:
> > In article

> >

> > > GIVEN A LIST OF SUBSETS OF N
> >
> > > you admit you cannot calculate ANY members of a supposed missing set.

Not without the complete list.

> >
> > > 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, of at least for one such missing set.

> > But there are more sets missing than not missing and 2 need not be

> > missing from every one of those "missing sets".

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

No missing set can be identified without first having the list of all
the sets which are not missing.

And then uncountably many of them will seen to be be missing.
--

[Graham Cooper]

On May 15, 6:14 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <0982dd8e-550d-4f48-a918-b9b7b3c00...@oy9g2000pbb.googlegroups.com>,

>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On May 15, 12:21 pm, Virgil <vir...@ligriv.com> wrote:
> > > In article
>
> > > > GIVEN A LIST OF SUBSETS OF N
>
> > > > you admit you cannot calculate ANY members of a supposed missing set.
>
> Not without the complete list.
>
>
>
>
>
>
>
>
>
>
>
> > > > 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, of at least for one such missing set.
> > > But there are more sets missing than not missing and 2 need not be
> > > missing from every one of those "missing sets".
>
> > So Missing Set = { ......... } ????
>
> No missing set can be identified without first having the list of all
> the sets which are not missing.
>

You can't calculate any members at all of any missing set ?

>
> And then uncountably many of them will seen to be be missing.
>

Can you define THAT set?


Herc

[Virgil]

In article
<237329e6-bd08-4bdf...@oy6g2000pbb.googlegroups.com>,

There is no natural which is necessarily a member of every missing set
so until you tell me a lot more about which naturals are or not in your
missing set, I cannot tell you anything about which naturals are or not
in your missing set.
>
>
> >
> > And then uncountably many of the sets will be seen to be be missing.

> >
>
> Can you define THAT set?

What set?
>
>
> Herc
--

[Graham Cooper]

On May 16, 10:32 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <237329e6-bd08-4bdf-94ce-c6eb87af6...@oy6g2000pbb.googlegroups.com>,

How many missing sets have you specified?


Herc

[Virgil]

In article
<027323ca-c76e-4a38...@j2g2000pbx.googlegroups.com>,

I haven't specified any of them. they get specified by anyone trying to
list all subsets of |N, as being the ones that aren't listed when he/she
is done.
--

[Graham Cooper]

On May 16, 1:10 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <027323ca-c76e-4a38-9fe3-05a7e9f97...@j2g2000pbx.googlegroups.com>,

If I list |N| subsets then I specify all the missing subsets?

Here you said:

If f(2) = { 1 , 5 , 11 } and f(3) = { 2 , 4 , 6, 8 , 10 , ... }

then 2 and 3 will be in that set, S.

What is set S?

Herc

[Virgil]

In article
<4fd8e46d-e4b7-4c80...@a10g2000pbr.googlegroups.com>,

I told you before at least twice that for any listing f:|N -> 2^|N the
set S = { n in |N : ~ n in f(n) } will not be not listed.

Is your memory failing?
--

[Graham Cooper]

On May 16, 2:51 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <4fd8e46d-e4b7-4c80-9d5e-c3338aeaa...@a10g2000pbr.googlegroups.com>,

Is S defined or specified?
[Y|N]

Can you calculate ANY values of S given f() so far????
[Y|N]


Herc

[Virgil]

In article
<8d9a4771-295b-445a...@li6g2000pbb.googlegroups.com>,

See above!

>
> Can you calculate ANY values of S given f() so far????
> [Y|N]
>

See above!
--

[Graham Cooper]

On May 16, 5:22 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <8d9a4771-295b-445a-a79c-e76558010...@li6g2000pbb.googlegroups.com>,

Given f so far

f(1) = { 1 , 3 , 6 }
f(2) = { 1 , 5 , 11 }
f(3) = { 2 , 4 , 6, 8 , 10 , ... }
f(4) = { 4 , 5, 6, 7, 8 }

what is S so far?

I know |f| and |S| are both infinite. No need to regurgitate that
irrelevant fact every post!

IS 1 e S ??
IS 2 e S ??
IS 3 e S ??
IS 3 e S ??

One would expect you to be able to instantiate the formula you post 20
times a day for 10 years!

Herc

[Virgil]

In article
<a26dbdcf-1b0b-4935...@oy9g2000pbb.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:

> On May 16, 5:22�pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <8d9a4771-295b-445a-a79c-e76558010...@li6g2000pbb.googlegroups.com>,
> > �Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > > On May 16, 2:51 pm, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > > <4fd8e46d-e4b7-4c80-9d5e-c3338aeaa...@a10g2000pbr.googlegroups.com>,
> > > > Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
> > > > > On May 16, 1:10 pm, Virgil <vir...@ligriv.com> wrote:
> > > > > > In article
> > > > > > <027323ca-c76e-4a38-9fe3-05a7e9f97...@j2g2000pbx.googlegroups.com>,
> > > > > > Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
> > > > > > > On May 16, 10:32 am, Virgil <vir...@ligriv.com> wrote:
> > > > > > > > In article
> > > > > > > > <237329e6-bd08-4bdf-94ce-c6eb87af6...@oy6g2000pbb.googlegroups.c

I have said several times already!

>
> I know |f| and |S| are both infinite. No need to regurgitate that
> irrelevant fact every post!
>
> IS 1 e S ??
> IS 2 e S ??
> IS 3 e S ??
> IS 3 e S ??

For the f above I have said several times already!

>
> One would expect you to be able to instantiate the formula you post 20
> times a day for 10 years!
>
> Herc

Except that there is no such formula, as there is no single thing that I
have posted 20 times in any one day of any 10 years.

ON the other hand, you post evidence of you ignorance every day.
--

[Graham Cooper]

On May 16, 5:45 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <a26dbdcf-1b0b-4935-b5d7-3688c0ed5...@oy9g2000pbb.googlegroups.com>,

You said

"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".

You also claim S is independent of f
unless f is explicitly stated for all N values (subsets of N).


All I want to know (after 3 days asking)

is WHAT IS THE MISSING SET that YOU SPECIFIED VIA S ?

I.e. actual VALUES - not ENGLISH ESSAYS.

AGAIN:

S = { ? , ? , ? , ? .... }

FILL IN THE BLANKS AS BEST YOU CAN!

USE the given f!

Herc

[Virgil]

In article
<9d1681d3-20a0-439e...@qz2g2000pbb.googlegroups.com>,
Graham Cooper <graham...@gmail.com> wrote:


> USE the given f!

You did not give any f.
--

[Graham Cooper]

On May 17, 10:00 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <9d1681d3-20a0-439e-bb2c-379c6f0ea...@qz2g2000pbb.googlegroups.com>,

>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > USE the given f!
>
> You did not give any f.
>

Can you use Cantor's Definition of missing set

on a Finite (sub) example or not?


Herc

[Graham Cooper]

On May 17, 10:00 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <9d1681d3-20a0-439e-bb2c-379c6f0ea...@qz2g2000pbb.googlegroups.com>,

>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > USE the given f!
>
> You did not give any f.
>

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

[Virgil]

In article
<2e280e67-4adf-45b4...@ks18g2000pbb.googlegroups.com>,

No, as anyone with any sense should have been able to work out for
himself.

In fact not even for an f undefined at only one argument, because any
such f's value may still be defined at any one of the many still missing
sets, which will then no longer be a missing set.

So one cannot tell which sets are not going to be used until one knows
which sets which will be used.

.
--

[Graham Cooper]

On May 17, 10:23 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <2e280e67-4adf-45b4-a320-330324f50...@ks18g2000pbb.googlegroups.com>,

>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On May 17, 10:00 am, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <9d1681d3-20a0-439e-bb2c-379c6f0ea...@qz2g2000pbb.googlegroups.com>,
> > > Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > USE the given f!
>
> > > You did not give any f.
>
> > Can you use Cantor's Definition of missing set
>
> > on a Finite (sub) example or not?
>
> No, as anyone with any sense should have been able to work out for
> himself.
>
> In fact not even for an f undefined at only one argument, because any
> such f's value may still be defined at any one of the many still missing
> sets, which will then no longer be a missing set.
>
> So one cannot tell which sets are not going to be used until one knows
> which sets which will be used.
>
>

Why did you say 2 & 3 were in S?


Herc

[AMiews]

"Graham Cooper" <graham...@gmail.com> wrote in message
news:b41aa06e-03cd-46fd...@a15g2000pbu.googlegroups.com...

set S = {a,b,c,......,F(N) } where n>4, F(N) = n

>Herc

Right or Wrong ?

[Virgil]

In article
<f00bc4a1-b109-45d2...@a10g2000pbr.googlegroups.com>,

I did not say that! I said that for the particular partial function you
gave they would have been in at least one such S but I also noted that
there could be many other S's in which neither need appear.

Do you ever bother to read what I post before making a fool of yourself
by misinterpreting it?
--

[Graham Cooper]

On May 17, 10:35 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <f00bc4a1-b109-45d2-9048-f359d2f2d...@a10g2000pbr.googlegroups.com>,

Yes, every post you make errors regarding Cantor's formula.

It's a real maze to get one sensible comment out of you.

You infer all sorts of facts given the example f
then say nothing can be inferred at all from a partial f.

Why would S change its value of 2eS

given f(2) but not f(100) ?

Herc

[Virgil]

In article
<b41aa06e-03cd-46fd...@a15g2000pbu.googlegroups.com>,

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).

Take your pick.
--

[Virgil]

In article
<fcb769a8-43d0-46c2...@qz2g2000pbb.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:

> Why would S change its value of 2eS
>
> given f(2) but not f(100) ?

You seem to think that there is only one non-image set S, but for any
function from |N to 2^|N there are more non-image sets in 2^|N than
image sets.
--

[Graham Cooper]

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).
>
> Take your pick.
>

Ahhh now we're getting somewhere!

f(5) = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ...... }

f(6) = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ...... }

f(7) = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ...... }


........


i.e

f(n) = N | n>4

Herc

[Virgil]

In article
<3fb4082c-a455-47a8...@qc10g2000pbb.googlegroups.com>,

Graham Cooper <graham...@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).
> >
> > Take your pick.
> >

Correction:

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 PROPER subset of |N other than f(3).

Take your pick.
--

[Graham Cooper]

On May 17, 11:17 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <3fb4082c-a455-47a8-a931-c219fd2fb...@qc10g2000pbb.googlegroups.com>,

Can you calculate CANTORS MISSING SET

given f ?

[Virgil]

In article
<dd2c208d-25d8-4a59...@li6g2000pbb.googlegroups.com>,

Any of

      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 PROPER subset of |N other than f(3).

Take your pick.

--

[Virgil]

In article
<3fb4082c-a455-47a8...@qc10g2000pbb.googlegroups.com>,

Graham Cooper <graham...@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.
`
--

[Graham Cooper]

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?

Your method (white box inspection) does not work for every possible f,
as such it is of no consequence.

GIVEN A SPECIFIC f, WHAT IS CANTORS MISSING SET?

All your answers are wrong!


Herc

[Virgil]

In article
<9d6b39cd-b349-4d9b...@ul7g2000pbc.googlegroups.com>,

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.
--

[Graham Cooper]

On May 17, 4:08 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <9d6b39cd-b349-4d9b-a34e-a759e81cb...@ul7g2000pbc.googlegroups.com>,

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

You can post *piffle* AFTER you've

CALCULATED_CANTORS_MISSING_SET


Herc

[Virgil]

In article
<908dc969-04a4-40d7...@a10g2000pbr.googlegroups.com>,

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.
--

[Alan Smaill]

Graham Cooper <graham...@gmail.com> writes:

> Yes, every post you make errors regarding Cantor's formula.
>
> It's a real maze to get one sensible comment out of you.
>
> You infer all sorts of facts given the example f
> then say nothing can be inferred at all from a partial f.
>
> Why would S change its value of 2eS
>
> given f(2) but not f(100) ?

Here's a game:

* you give me a way of determining the nth digit of the mth number
in a list of reals given in decimal;
* I give you back a way of determining the digits of a real in decimal;
* you tell me where that number is in your given list --
you win if it is where you claim, and lose otherwise.

Do you want to play?


> Herc

--
Alan Smaill

[Graham Cooper]

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

> <908dc969-04a4-40d7-acdd-2b0ac5791...@a10g2000pbr.googlegroups.com>,

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.

----------

Does your favorite Cantors formula

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

[Graham Cooper]

On May 17, 7:46 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

If you allow a hypothetical Halt function then OK

TM_n is the nTH Turing Machine

UTM( n , pos ) = TM_n(pos)

UHM( h , pos ) = UTM( n , pos )

WHERE TM_n is the hTH TM that halts on all inputs

DUHM( h , pos ) = UHM( h , pos ) MOD 10

R = { r(n) | r(n)= SUMi ( DUHM( n , i ) * 1/10^i ) }


Herc

--
A new kid goes to school each day but on the way
to the lunch canteen a Bully stops him like so:

[MONDAY]
BULLY: I'm thinking of a number from 1 - 10
KID : 7 ?
BULLY : NO! It was 8! [takes lunch money]

[TUESDAY]
BULLY: I'm thinking of a number from 1 - 10
KID : 5 ?
BULLY : NO! It was 6! [takes lunch money]

[WEDNESDAY]
BULLY: I'm thinking of a number from 1 - 10
KID : 1 ?
BULLY : NO! It was 2! [takes lunch money]

[THURSDAY]
BULLY: I'm thinking of a number from 1 - 10
KID : 3 ?
BULLY : NO! It was 4! [takes lunch money]

[FRIDAY]
BULLY: I'm thinking of a number from 1 - 10
KID : 9 ?
BULLY : NO! It was 10! [takes lunch money]

--------------
Cantor uses this SAME BULLY TRICK.
Whatever Number you Get - I'll Change it X INFINITY!

[Alan Smaill]

Graham Cooper <graham...@gmail.com> writes:

> On May 17, 7:46 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> Graham Cooper <grahamcoop...@gmail.com> writes:
>> > Yes, every post you make errors regarding Cantor's formula.
>>
>> > It's a real maze to get one sensible comment out of you.
>>
>> > You infer all sorts of facts given the example f
>> > then say nothing can be inferred at all from a partial f.
>>
>> > Why would S change its value of 2eS
>>
>> > given f(2) but not f(100) ?
>>
>> Here's a game:
>>
>> * you give me a way of determining the nth digit of the mth number
>>   in a list of reals given in decimal;
>> * I give you back a way of determining the digits of a real in decimal;
>> * you tell me where that number is in your given list --
>>   you win if it is where you claim, and lose otherwise.
>>
>> Do you want to play?
>>
>
> If you allow a hypothetical Halt function then OK

No, you need to start by giving an effective way of computing
the nth digit of the mth real.

Do you want to play?

> Herc
>


--
Alan Smaill

[Graham Cooper]

OK,

max=1 GOOGEL

TM_n_max(pos) = t
iff

TM_n(pos) = t
and halts in less than max*2^pos*2^n state transitions

TM_n(pos) = 0
otherwise


UTM_max( n , pos ) = TM_n_max(pos)
UHM( h , pos ) = UTM_max( h , pos )

[Virgil]

In article
<7c34c1bd-ae57-4e19...@a10g2000pbr.googlegroups.com>,

Thus Cantor will always win! But that is, as we have learned to expect
from Cantor's critics, a false analogy because Cantor explains his rule
first before any numbers are chosen and holds to it.
--

[Graham Cooper]

On May 18, 10:25 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <7c34c1bd-ae57-4e19-8259-5f5a34574...@a10g2000pbr.googlegroups.com>,

Only in your imagination.

Stray formulas do not form a SET of defined LIMIT values.

In DEFINITIONAL SET THEORY the OPPOSITE
of AXIOM OF CHOICE holds.

~A.O.C.

EXIST(SET) with All ELEMENTS Defined
-> EXIST(ELEMENT)



Herc

[Virgil]

In article
<ca34a387-11e5-477f...@qz2g2000pbb.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:


> > 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.
>
> ----------
>
> Does your favorite Cantors formula

It is not my formula at all, but Cantor's

>
> S = { n | n ~e f(n) }
>
> WORK on the GIVEN f ?
>
> If it does - WHAT IS S ?

For the given f, ask yourself:
Is 1 in f(1)?
Is 2 in f(2)?
Is 3 in f(3)?
Is 4 in f(4)?
Is n in f(n) for n > 4?
And then work out which will be in { n in |N : ~ n in f(n) }.

And if you can't, why should anyone want to spoil such perfect
ignorance?

>
>
> ------------
>
> Not interested in any other missing sets or explanations ABOUT S.
>
> JUST WHAT IS S given that f ?
>

Why should anyone want to spoil your perfect ignorance?
--

[Graham Cooper]

On May 18, 10:34 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <ca34a387-11e5-477f-9115-f5a1ce2fd...@qz2g2000pbb.googlegroups.com>,

>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>
> > > 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.
>
> > ----------
>
> > Does your favorite Cantors formula
>
> It is not my formula at all, but Cantor's
>
>
>
> > S = { n | n ~e f(n) }
>
> > WORK on the GIVEN f ?
>
> > If it does - WHAT IS S ?

For the given f, ask yourself:

Is 1 in f(1)? YES
Is 2 in f(2)? NO
Is 3 in f(3)? NO
Is 4 in f(4)? YES
Is n in f(n) for n > 4? YES to ALL

> And then work out which will be in { n in |N : ~ n in f(n) }.

I get S = { 2 , 3 }

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

  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

You took 5 days and still couldn't calculate Cantors Missing Set.

Herc

[Virgil]

In article
<38a76ce0-667e-4617...@wg15g2000pbb.googlegroups.com>,

Actually I posted that set long ago, but you were to dumb to realize
what it was.
--

[Virgil]

In article
<babda6ce-964b-4906...@fz1g2000pbb.googlegroups.com>,

Graham Cooper <graham...@gmail.com> wrote:

> In DEFINITIONAL SET THEORY the OPPOSITE
> of AXIOM OF CHOICE holds.

But I am not compelled to limit myself to any of your corrupt and
corrupting rules about sets.
--

[Graham Cooper]

On May 18, 10:47 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <38a76ce0-667e-4617-80a2-a8ab35dec...@wg15g2000pbb.googlegroups.com>,

[VIRGIL]

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).

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

NOPE! You posted WRONG and IRRELEVANT RUBBISH!

Herc

[Graham Cooper]

On May 18, 10:50 am, Virgil <vir...@ligriv.com> wrote:
> In article

> <babda6ce-964b-4906-89d8-704981a2d...@fz1g2000pbb.googlegroups.com>,

>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > In DEFINITIONAL SET THEORY the OPPOSITE
> > of AXIOM OF CHOICE holds.
>
> But I am not compelled to limit myself to any of your corrupt and
> corrupting rules about sets.
>

Then you have no definitions of the members of R

and imagine the LIMIT exists in your imaginary infinite sums.

Herc

[Alan Smaill]

Graham Cooper <graham...@gmail.com> writes:

>> No, you need to start by giving an effective way of computing
>> the nth digit of the mth real.
>>
>> Do you want to play?
>>
>> > Herc
>>
>> --
>> Alan Smaill
>
> OK,

You'll need to be less cryptic:

> max=1 GOOGEL

googol?

> TM_n_max(pos) = t
> iff
>
> TM_n(pos) = t
> and halts in less than max*2^pos*2^n state transitions
>
> TM_n(pos) = 0
> otherwise

Do you have an effectively given listing of Turing machines,
of which TM_n is the nth?

What is the language of these TMs? in particular, what values for t above?

> UTM_max( n , pos ) = TM_n_max(pos)
> UHM( h , pos ) = UTM_max( h , pos )
> DUHM( h , pos ) = UHM( h , pos ) MOD 10

and this is meant to give decimal digit of the hth entry
at position pos?

>
> R = { r(n) | r(n)= SUMi ( DUHM( n , i ) * 1/10^i ) }

Do you claim that all computable reals (in the interval [0,1])
will appear in this listing?

>
>
> Herc

--
Alan Smaill

[Graham Cooper]

On May 23, 4:27 am, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

> Graham Cooper <grahamcoop...@gmail.com> writes:
> >> No, you need to start by giving an effective way of computing
> >> the nth digit of the mth real.
>
> >> Do you want to play?
>
> >> > Herc
>
> >> --
> >> Alan Smaill
>
> > OK,
>
> You'll need to be less cryptic:
>
> > max=1 GOOGEL
>
> googol?
>
> > TM_n_max(pos) = t
> > iff
>
> > TM_n(pos) = t
> > and halts in less than max*2^pos*2^n state transitions

enough iterations are allowed for exponential complexity
on turing machine size and input size combined.

i.e. TM_1000(500)

has

1 GOOGOL X 2^500^ 2^1000 run time until it just outputs 0

>
> > TM_n(pos) = 0
> > otherwise
>
> Do you have an effectively given listing of Turing machines,
> of which TM_n is the nth?
>

A method for representing all possible TURING MACHINES that indexes
them

TM1, TM2, TM3..

The first 8 TMs are all size 1 with only 1 internal state the starting
state S, where each state has 2 branches: INPUT-0 and INPUT-1

TM-1
S-00L->S
S-10L->S

TM-2
S-00L->S
S-10R->S
...

TM-8
S-11R->S
S-01R->S

--------

Next comes TM-9, the first 2 State TM.

TM-9
S-00L->1
S-10L->1
2-00L->S
2-10L->S
..

> What is the language of these TMs? in particular, what values for t above?
>
> > UTM_max( n , pos ) = TM_n_max(pos)
> > UHM( h , pos ) = UTM_max( h , pos )
> > DUHM( h , pos ) = UHM( h , pos ) MOD 10
>
> and this is meant to give decimal digit of the hth entry
> at position pos?
>

Yes

>
>
> > R = { r(n) | r(n)= SUMi ( DUHM( n , i ) * 1/10^i ) }
>
> Do you claim that all computable reals (in the interval [0,1])
> will appear in this listing?
>
>

No.


Herc

[Alan Smaill]

thanks for clarifications.

Graham Cooper <graham...@gmail.com> writes:

> On May 23, 4:27 am, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> Graham Cooper <grahamcoop...@gmail.com> writes:
>> >> No, you need to start by giving an effective way of computing
>> >> the nth digit of the mth real.
>>
>> >> Do you want to play?
>>

>> Do you have an effectively given listing of Turing machines,
>> of which TM_n is the nth?
>>
>
>
> A method for representing all possible TURING MACHINES that indexes
> them
>
> TM1, TM2, TM3..
>
> The first 8 TMs are all size 1 with only 1 internal state the starting
> state S, where each state has 2 branches: INPUT-0 and INPUT-1

OK

>> What is the language of these TMs? in particular, what values for t above?

I take it the alphabet is decimal digits then, and output
can be read as natural numbers.

>> > UTM_max( n , pos ) = TM_n_max(pos)
>> > UHM( h , pos ) = UTM_max( h , pos )
>> > DUHM( h , pos ) = UHM( h , pos ) MOD 10
>>
>> and this is meant to give decimal digit of the hth entry
>> at position pos?
>
> Yes
>

>> Do you claim that all computable reals (in the interval [0,1])
>> will appear in this listing?
>
> No.

And you see it's easy to give you a TM that will give the digits
of a real not in your list?

> Herc

--
Alan Smaill

[Graham Cooper]

I though we were playing

HERC: number 3
ALAN: no 4

HERC: number 8
ALAN: no 9

HERC: number 9
ALAN: no 1

AD INFINITUM?


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

OK I give up, if you input a tessellation string based on the input
digit and output that digit of pi then the domain may fall outside
10^100 * 2^n * 2^pos processing cycles.


Herc
--
www.BLoCKPROLOG.com

[Alan Smaill]

Graham Cooper <graham...@gmail.com> writes:

> On May 23, 7:35 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> >> Do you claim that all computable reals (in the interval [0,1])
>> >> will appear in this listing?
>>
>> > No.
>>
>> And you see it's easy to give you a TM that will give the digits
>> of a real not in your list?
>>
>
>
> I though we were playing
>
> HERC: number 3
> ALAN: no 4
>
> HERC: number 8
> ALAN: no 9
>
> HERC: number 9
> ALAN: no 1
>
> AD INFINITUM?

No, the game was:

you give a way to prescribe the nth digit of the mth
real;
I give you back a way to prescribe the nth digit of a particular real;
If that real is in your list you win, otherwise you lose.

> -------------
>
> OK I give up, if you input a tessellation string based on the input
> digit and output that digit of pi then the domain may fall outside
> 10^100 * 2^n * 2^pos processing cycles.

Yes, the argument that it can't be done in general
is pretty robust.

>
> Herc
> --
> www.BLoCKPROLOG.com

--
Alan Smaill

[Graham Cooper]

On May 24, 7:10 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

actually its entirely childish and just goes around in 5 mutually
supporting circular arguments, each vertex of the pentagon more
ludicrous than the next.

you'd want it to be more than pretty robust to declare E(X) X>oo
in every logic proof ever written in every academic institution,.


Herc
--
www.BLoCKPROLOG.com

[Alan Smaill]

You didn't find a way out of the version above, though.

> you'd want it to be more than pretty robust to declare E(X) X>oo
> in every logic proof ever written in every academic institution,.

A good thing that people don't claim some that there is
an X bigger than infinity, then.

[Graham Cooper]

2 more erroneous claims.

|R| > | infinite list rows |


Herc