Matheology § 269

[WM]

Matheology § 269

How to distinguish a decimal representation from a set of all
terminating decimal representations?
It seems impossible to accomplish this task by means of one ore
more digits that have finite indices, i.e., finite distances from the
decimal point.
It is clear that an infinite decimal representation has more digits
than every finite one. But it is as clear that there are not more
finite indices than all finite indices which are already used and
occupied by all possible sequences of digits to produce all finite
decimal representations.
Is it possible to apply other tools?

Regards, WM

[Newberry]

If I understand this you are saying that there is no natural number n such that digit[n] of the antidiagonal differs from digit[n] of any sequence on the enumerated list.

This seems to be a correct assertion.

[AMiews]

"WM" <muec...@rz.fh-augsburg.de> wrote in message
news:5bfcdad2-35d5-46f7...@v3g2000vbr.googlegroups.com...

Matheology � 269

>How to distinguish a decimal representation from a set of all
>terminating decimal representations?

what is "terminating" ? all the rest are Zeros ? or a repeating pattern ?

what is non-terminating ?

> It seems impossible to accomplish this task by means of one ore
>more digits that have finite indices, i.e., finite distances from the
>decimal point.

need your definition of "terminating" first

> It is clear that an infinite decimal representation has more digits
>than every finite one.

wrong. It is simply convention to leave off all the Zeros, or put a bar
above the section that repeates.
All decimal representations have infinite number of digits, there are no
finite ones.

>But it is as clear that there are not more
>finite indices than all finite indices which are already used and
>occupied by all possible sequences of digits to produce all finite
>decimal representations.
> Is it possible to apply other tools?

you need to correct your mistakes first before we proceed further.

>Regards, WM

[WM]

No, that is not the point. The point is that there is no sequence of
digits with only finite indices that differs from all terminating
sequences. The point is that it is impossible to distinguish the
antidiagonal of a Cantor list from all entries of the list.

If the list contains all rational numbers of the unit interval (which
should be possible) then the antidiagonal up to every digit d_n is in
the list (infinitely often)
forall n: d_1, d_2, ..., d_n is in the list below line n.
(Proof necessary?)

And if we have a decimal representation a = SUM a_n*10^-n such that
forall n: a_n = d_n,
is then a = d? If not, how can we distinguish a from d?

Regards, WM

[Virgil]

In article
<5bfcdad2-35d5-46f7...@v3g2000vbr.googlegroups.com>,

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

> Matheology � 269
>
> How to distinguish a decimal representation from a set of all
> terminating decimal representations?

A decimal representation does not contain any members, while every
nonempty set does.
--

[Virgil]

In article <17887d48-5fda-401b...@googlegroups.com>,

Newberry <newbe...@gmail.com> wrote:

> > How to distinguish a decimal representation from a set of all
> >
> > terminating decimal representations?

Every terminating decimal has a natural number position for its last
nonzero digit. Every non-terminating decimal lacks any such natural.
--

[Virgil]

In article
<9c78ef5b-eb3e-4189...@k6g2000yqh.googlegroups.com>,

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

> On 23 Mai, 16:03, Newberry <newberr...@gmail.com> wrote:
> > On Thursday, May 23, 2013 3:11:55 AM UTC-7, WM wrote:
> > > Matheology � 269
> >
> > > How to distinguish a decimal representation from a set of all
> >
> > > terminating decimal representations?
> >
> > > � �It seems impossible to accomplish this task by means of one ore
> >
> > > more digits that have finite indices, i.e., finite distances from the
> >
> > > decimal point.
> >
> > > � �It is clear that an infinite decimal representation has more digits
> >
> > > than every finite one. But it is as clear that there are not more
> >
> > > finite indices than all finite indices which are already used and
> >
> > > occupied by all possible sequences of digits to produce all finite
> >
> > > decimal representations.
> >
> > > � �Is it possible to apply other tools?
> >
> > > Regards, WM
> >
> > If I understand this you are saying that there is no natural number n such
> > that digit[n] of the antidiagonal differs from digit[n] of any sequence on
> > the enumerated list.
>
> No, that is not the point. The point is that there is no sequence of
> digits with only finite indices that differs from all terminating
> sequences. The point is that it is impossible to distinguish the
> antidiagonal of a Cantor list from all entries of the list.

It is quite possible to distinguish any anti-diaganal from each entry in
the list. At least everywhere not ruled by WMytheology.

>
> If the list contains all rational numbers of the unit interval (which
> should be possible) then the antidiagonal up to every digit d_n is in
> the list (infinitely often)
> forall n: d_1, d_2, ..., d_n is in the list below line n.
> (Proof necessary?)

Proof by WM would be impossible even if the claim were true!

>
> And if we have a decimal representation a = SUM a_n*10^-n such that
> forall n: a_n = d_n

But the antidiagonal construction prevents any such result, so WM is
dreamwalking again!.
--

[AMiews]

"Virgil" <vir...@ligriv.com> wrote in message
news:virgil-77E0DB....@BIGNEWS.USENETMONSTER.COM...

there is no difference between the two,
Just the common convention of not writing the rest of the zeros down, (it
would take too long)
it is only shorthand

[Newberry]

I meant to say that for any n there is sequence S on the list such that (Ai<=n)(S_d[i] = D_d[i]), where S_d[i] is the i-th digit of a sequence and D_d[i] is the i-th digit of the anti-diagonal. I do not know if this is what you meant.
>
>
> Regards, WM

[Virgil]

In article <af5016e5-72ec-4d31...@googlegroups.com>,

Newberry <newbe...@gmail.com> wrote:

> > And if we have a decimal representation a = SUM a_n*10^-n such that
> >
> > forall n: a_n = d_n,

Then either a was not listed at all or you erred in your selection of
the d_n.
--

[Virgil]

In article <knmfrv$bio$1...@news.albasani.net>,

Either a positive real number has a decimal representation with a last
non-zero digit and is of form a/10^n for some naturals a and n or does
not have a terminating decimal representation.

That is the very true difference between the two.
--

[Zeit Geist]

On Thursday, May 23, 2013 1:53:38 PM UTC-7, WM wrote:

> On 23 Mai, 16:03, Newberry <newberr...@gmail.com> wrote:
>
> > On Thursday, May 23, 2013 3:11:55 AM UTC-7, WM wrote:
>
> > > Matheology § 269
>
> >
>
> > > How to distinguish a decimal representation from a set of all
>
> >
>
> > > terminating decimal representations?
>
> >
>
> > >    It seems impossible to accomplish this task by means of one ore
>
> >
>
> > > more digits that have finite indices, i.e., finite distances from the
>
> >
>
> > > decimal point.
>
> >
>
> > >    It is clear that an infinite decimal representation has more digits
>
> >
>
> > > than every finite one. But it is as clear that there are not more
>
> >
>
> > > finite indices than all finite indices which are already used and
>
> >
>
> > > occupied by all possible sequences of digits to produce all finite
>
> >
>
> > > decimal representations.
>
> >
>
> > >    Is it possible to apply other tools?
>
> >
>
> > > Regards, WM
>
> >
>
> > If I understand this you are saying that there is no natural number n such that digit[n] of the antidiagonal differs from digit[n] of any sequence on the enumerated list.
>
>
>
> No, that is not the point. The point is that there is no sequence of
>
> digits with only finite indices that differs from all terminating
>
> sequences. The point is that it is impossible to distinguish the
>
> antidiagonal of a Cantor list from all entries of the list.
>

If a real number, r, is on the j-th line of the list,
then the j-th digit of the antidiagonal, d, is not equal
to the j-th digit of r.

Given any j e |N, with r on line j; r_j ~= d_j.

Hence, every and all entries of the list differ from the antidiagonal.

>
> If the list contains all rational numbers of the unit interval (which
>
> should be possible) then the antidiagonal up to every digit d_n is in
>
> the list (infinitely often)
>
> forall n: d_1, d_2, ..., d_n is in the list below line n.
>
> (Proof necessary?)
>

Yes, we do have all FIS of d somewhere in the list.
There is line containing d(1) = ( d_1 ), as it is a rational.
We can also append any terminating decimal to it,
and find infinitely many numbers r, such that ( r_1 ) = ( d_1).

This can be done for every n e |N. Also, there are infinite number
of them below line n, since there are an infinite number of them
in total and only a finite number of them can be above line n.

Thus, we can choose one representative for each n and define a sequence,
( x_n | n e |N ) where FIS_n( x_n ) = FIS_n ( d ).

However, for each x_n ( regardless of which was chosen for the sequence )
we have x_n ~= d, since there exist an m e |N such that (x_n)_m ~= d_m.
This number being the line number of x_n, which is greater than n.

>
> And if we have a decimal representation a = SUM a_n*10^-n such that
>
> forall n: a_n = d_n,
>
> is then a = d? If not, how can we distinguish a from d?
>

Yes, but for all a in the list a_m ~= d_m, where m is the line number of a.

Also,

1. For all n e |N, the exist x_n, such that FIS(n)(x_n) = FIS(n)(d),

dose not necessarily imply that

2. There exist x, such that for all n e |N, FIS(n)(x) = FIS(n)(d).

Now, if the sequence (x_n), all the FIS of d in order, defines a
topologically closed set, then d, the accumulation point of (x_n)
will be in the sequence. However, since (x_n) is eventually
increasing for all n e |N, it can't possibly be closed.

If you can show that 1. implies 2. for this particular case,
then you have your contradiction.

>
> Regards, WM

[Zeit Geist]

On Friday, May 24, 2013 11:47:41 AM UTC-7, Zeit Geist wrote:

> 1. For all n e |N, the exist x_n, such that FIS(n)(x_n) = FIS(n)(d),
>
> dose not necessarily imply that
>
> 2. There exist x, such that for all n e |N, FIS(n)(x) = FIS(n)(d).
>

I should note that I meant we can't prove the existence of x in
the sequence (x_n), necessarily.


ZG

[WM]

On 24 Mai, 04:46, Newberry <newberr...@gmail.com> wrote:

> I meant to say that for any n there is sequence S on the list such that (Ai<=n)(S_d[i] = D_d[i]), where S_d[i] is the i-th digit of a sequence and D_d[i] is the i-th digit of the anti-diagonal. I do not know if this is what you meant.

Yes, that is precisely what I meant. For every n! (I had thought
erroneously that you only accepted that every S somewhere differs from
D, which is also correct, but is not what I emphasized.)

Regards, WM

[Virgil]

In article
<cda5673f-07a1-4919...@m18g2000vbo.googlegroups.com>,

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

> On 24 Mai, 04:46, Newberry <newberr...@gmail.com> wrote:
>
> > I meant to say that for any n there is sequence S on the list such that
> > (Ai<=n)(S_d[i] = D_d[i]), where S_d[i] is the i-th digit of a sequence and
> > D_d[i] is the i-th digit of the anti-diagonal. I do not know if this is
> > what you meant.
>
> Yes, that is precisely what I meant.

Do you have anything like a proof that than even can occur?
--

[WM]

On 24 Mai, 20:47, Zeit Geist <tucsond...@me.com> wrote:

> If a real number, r, is on the j-th line of the list,
> then the j-th digit of the antidiagonal, d, is not equal
> to the j-th digit of r.

Correct.

>
> Given any j e |N, with r on line j; r_j ~= d_j.
>
> Hence, every and all entries of the list differ from the antidiagonal.

Yes, every entry differs from the antidiagonal.

>
>
>
> > If the list contains all rational numbers of the unit interval (which
>
> > should be possible) then the antidiagonal up to every digit d_n is in
>
> > the list (infinitely often)
>
> > forall n: d_1, d_2, ..., d_n is in the list below line n.
>
> > (Proof necessary?)
>
> Yes, we do have all FIS of d somewhere in the list.

So no proof necessary.

> There is line containing d(1) = ( d_1 ), as it is a rational.
> We can also append any terminating decimal to it,
> and find infinitely many numbers r, such that ( r_1 ) =  ( d_1).
>
> This can be done for every n e |N.  Also, there are infinite number
> of them below line n, since there are an infinite number of them
> in total and only a finite number of them can be above line n.
>
> Thus, we can choose one representative for each n and define a sequence,
> ( x_n | n e |N ) where FIS_n( x_n ) = FIS_n ( d ).
>
> However, for each x_n ( regardless of which was chosen for the sequence )
> we have x_n ~= d, since there exist an m e |N such that (x_n)_m ~= d_m.
> This number being the line number of x_n, which is greater than n.

Therefore there is a contradiction.
Forall n: FIS_n( x_n ) = FIS_n ( d )
means that no digit of d can be found that differs from all FIS_n.

> > And if we have a decimal representation a = SUM a_n*10^-n such that
>
> > forall n: a_n = d_n,
>
> > is then a = d? If not, how can we distinguish a from d?
>
> Yes, but for all a in the list a_m ~= d_m, where m is the line number of a.

Yes. But that does not invalidate my result. It only shows that there
is a contradiction if "all" is put for "every", if actual infinity is
put instead of potential infinity.

>
> Also,
>
> 1.  For all n e |N, the exist x_n, such that FIS(n)(x_n) = FIS(n)(d),
>
> dose not necessarily imply that
>
> 2.  There exist x, such that for all n e |N, FIS(n)(x) = FIS(n)(d).

Then give a counter example.

>
> Now, if the sequence (x_n), all the FIS of d in order, defines a
> topologically closed set, then d, the accumulation point of (x_n)
> will be in the sequence.  However, since (x_n) is eventually
> increasing for all n e |N, it can't possibly be closed.
>
> If you can show that 1. implies 2. for this particular case,
> then you have your contradiction.

No. I know that in mathematics
for all n: a_n = d_n
means a = d

If you can find an exception of this rule, state it. I have no reason
to prove anything else.

Regards, WM

[WM]

And we can't prove the existence of d either. In fact an infinite
sequence of digits cannot exist other than as a finite formula. But
there are only countably many finite formulas.

Regards, WM

[Virgil]

In article
<111378fd-4e54-4dca...@bh5g2000vbb.googlegroups.com>,

Then unless WM can list every one of these finite formula and show that
none of them work here, his idiot claims remain unproven and unprovable.

But Cantor's finite formula works fine!
>
> Regards, WM
--

[Virgil]

In article
<262df99c-46a5-4792...@dl10g2000vbb.googlegroups.com>,

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

> No. I know that in mathematics
> for all n: a_n = d_n
> means a = d

Where does a come from? It is certainly not in the list from which d is
generated, so that it is unlisted, and again proves any list to be
incomplete.
--

[WM]

On 25 Mai, 09:46, Virgil <vir...@ligriv.com> wrote:
> In article
> <262df99c-46a5-4792-b673-c76e0d981...@dl10g2000vbb.googlegroups.com>,

>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > No. I know that in mathematics
> > for all n: a_n = d_n
> > means a = d
>
> Where does a come from? It is certainly not in the list from which d is
> generated, so that it is unlisted, and again proves any list to be
> incomplete.
> --

a_n is not coming from anywhere. This equation simply shows that a
number that is identical at every digit with another number simply is
this number. And since the list contains infinitely many numbers which
are identical for every n with d_1, ..., d_n, the diagonal is
infinitely often listed. - Iff it was not meaningless to speak of a
complete list.

Regards, WM

[Newberry]

I originally misstated it. But anyway this is an interesting point. Does ZFC imply the existence of infinite natural numbers?
>
>
>
> Regards, WM

[WM]

No, it does not. Therefore we have exhausted the digit sequence
(d_n)and shown that a = d if for all natural indexes a_n = d_n.
Likewise the complete anti-diagonal number d is established if for
every line with finite number n we have created a digit d_n. There is
no talking about a limit, because this limit would also kill Cantor's
argument. Example:
Forall n: 1/n =/= 0.000....
But that would not hold in the limit 0 of the sequence (1/n).

Regards, WM

[Virgil]

In article
<6d15cc85-418d-4004...@k3g2000vbn.googlegroups.com>,

You are claiming that two infinite digit sequences which agree for a
large enough but finite number of places must be equal, but that can
only hold true under the rules of WMytheology, and definitely does not
hold not under the rules of mathematics.

So WM is WRONG!
AGAIN!!
AS USUAL!!!

- Iff it was not meaningless to speak of a
> complete list.
>
> Regards, WM

--

[Virgil]

In article
<7cab0fe2-8fbe-4947...@gw5g2000vbb.googlegroups.com>,

Cantor has two totally different proofs showing why the set of real
numbers cannot be covered by any listing of its members, and nothing
that WM has shown or can show in any way falsifies either of those
proofs.

Example:
> Forall n: 1/n =/= 0.000....
> But that would not hold in the limit 0 of the sequence (1/n).
>
> Regards, WM

--

[WM]

On 25 Mai, 22:32, Virgil <vir...@ligriv.com> wrote:

>> since the list contains infinitely many numbers which
> > are identical for every n with d_1, ..., d_n, the diagonal is
> > infinitely often listed.
>
> You are claiming that two infinite digit sequences which agree for a
> large enough but finite number of places must be equal,

No, I claim that two infinite digit sequences
a_1,a_2,a_3... and d_1, d_2, d_3...
which agree for every digit such that

forall n: a_n = d_n

(this follows from
forall n: a_1,a_2,a_3,...,a_n = d_1, d_2, d_3,...,d_n,)
define the same number.

Matheology requires more than every n. That's why it fails.

Regards, WM

[WM]

On 25 Mai, 22:45, Virgil <vir...@ligriv.com> wrote:

> Cantor has two totally different proofs showing why the set of real
> numbers cannot be covered by any listing of its members,

Of course that is true. Had he not uttered the weird idea that
infinite sets could be finished and completely listed, nobody would
care.

Regards, WM

[Sam Sung]

Idiot WM babbles:

ROFL - Cantor did not state that infinite sets "could be finished".

[WM]

On 26 Mai, 10:19, Sam Sung <n...@mail.invalid> wrote:
> Idiot WM babbles:
>
> > On 25 Mai, 22:45, Virgil <vir...@ligriv.com> wrote:
>
> >> Cantor has two totally different proofs showing why the set of real
> >> numbers cannot be covered by any listing of its members,
>
> > Of course that is true. Had he not uttered the weird idea that
> > infinite sets could be finished and completely listed, nobody would
> > care.
>

> Cantor did not state that infinite sets "could be finished".

How should omega + 1 > omega, if omega was not finished?

Some of Cantor's writings:

die Sache verhält sich, wie man im folgenden deutlich sehen wird, in
Wahrheit so, daß zu einer unendlichen Zahl, wenn sie als bestimmt und
vollendet gedacht wird, sehr wohl eine endliche hinzugefügt ...

Zu dem Gedanken, das Unendlichgroße nicht bloß in der Form des
unbegrenzt Wachsenden und in der hiermit eng zusammenhängenden Form
der im siebzehnten Jahrhundert zuerst eingeführten konvergenten
unendlichen Reihen zu betrachten, sondern es auch in der bestimmten
Form des Vollendet-unendlichen mathematisch durch Zahlen zu fixieren,
bin ich fast wider meinen Willen, weil im Gegensatz zu mir
wertgewordenen Traditionen, durch den Verlauf vieljähriger
wissenschaftlicher Bemühungen und Versuche logisch gezwungen worden,
und ich glaube daher auch nicht, daß Gründe sich dagegen werden
geltend machen lassen, denen ich nicht zu begegnen wüßte.

Wundt's Auseinandersetzung zeigt, daß er sich des fundamentalen
Unterschieds von Uneigentlichunendlichem = veränderlichem Endlichem =
synkategorematice infinitum einerseits und Eigentlichunendlichem =
Transfinitum = Vollendetunendlichem = Unendlichseiendem =
kategorematice infinitum andrerseits nicht klar und deutlich bewußt
ist;

Viele weitere Stellen könnten angeführt werden, aber zur Widerlegung
einer falschen Behauptung genügt ja schon ein Beispiel.

Concluding remark: It is obvious that most matheologians do not know
the foundations of matheology.

Gruß, WM

[Sam Sung]

>> Idiot WM babbles:

>> Cantor did not state that infinite sets "could be finished".
>
> How should omega + 1 > omega, if omega was not finished?
>
> Some of Cantor's writings:
>

> die Sache verh�lt sich, wie man im folgenden deutlich sehen wird, in
> Wahrheit so, da� zu einer unendlichen Zahl, wenn sie als bestimmt und
> vollendet gedacht wird, sehr wohl eine endliche hinzugef�gt ...

Yes ... sehr wohl eine endliche hinzugef�gt WERDEN KANN

> Zu dem Gedanken, das Unendlichgro�e nicht blo� in der Form des
> unbegrenzt Wachsenden und in der hiermit eng zusammenh�ngenden Form
> der im siebzehnten Jahrhundert zuerst eingef�hrten konvergenten

> unendlichen Reihen zu betrachten, sondern es auch in der bestimmten
> Form des Vollendet-unendlichen mathematisch durch Zahlen zu fixieren,
> bin ich fast wider meinen Willen, weil im Gegensatz zu mir

> wertgewordenen Traditionen, durch den Verlauf vielj�hriger
> wissenschaftlicher Bem�hungen und Versuche logisch gezwungen worden,
> und ich glaube daher auch nicht, da� Gr�nde sich dagegen werden
> geltend machen lassen, denen ich nicht zu begegnen w��te.

Yes, infinite convergent sequences are "ready" in this way.

> Concluding remark: It is obvious that most matheologians

> ...matheology

You filthy pig (mieses Dreckschwein) should not be answered
as long as you insult sane folks using matheology.

Piss of you brainsick, megalomaniac, motherfucking rat.

WE PISS INTO YOUR FILTHY FACE. GO DIE, RAT.

[Sam Sung]

Idiot WM babbles:

>>> Idiot WM babbles:
>
>>> Cantor did not state that infinite sets "could be finished".
>>
>> How should omega + 1 > omega, if omega was not finished?
>>
>> Some of Cantor's writings:
>>
>> die Sache verh�lt sich, wie man im folgenden deutlich sehen wird, in
>> Wahrheit so, da� zu einer unendlichen Zahl, wenn sie als bestimmt und
>> vollendet gedacht wird, sehr wohl eine endliche hinzugef�gt ...
>
> Yes ... sehr wohl eine endliche hinzugef�gt WERDEN KANN

This simply means "oo + n = 00".

[Sam Sung]

Idiot WM babbles:

>>> Idiot WM babbles:
>
>>> Cantor did not state that infinite sets "could be finished".
>>
>> How should omega + 1 > omega, if omega was not finished?
>>
>> Some of Cantor's writings:
>>
>> die Sache verh�lt sich, wie man im folgenden deutlich sehen wird, in
>> Wahrheit so, da� zu einer unendlichen Zahl, wenn sie als bestimmt und
>> vollendet gedacht wird, sehr wohl eine endliche hinzugef�gt ...
>
> Yes ... sehr wohl eine endliche hinzugef�gt WERDEN KANN

This simply means "oo + n = oo" (where "oo" means "card(infinite set)" ).

[fom]

The "finished set" is a term that Cantor introduced to
distinguish arbitrary totalities from the inconsistent
multiplicities that could not be formed.

The real issue with Cantor's work would seem to be the
relationship of logic to mathematics. For example,
Kant makes a statement along the lines of the
paraphrase "the singular judgement is to the universal
judgement as an individual is to infinity". In this
construal, infinity arises by addressing the nature
of "universes of discourse" as criticism of mathematics
leads to logical solutions.

Of course, this is not so apparent in Cantor's work as
it would be if used to describe Frege and Russell. But,
with Dedekind and Cantor, the issue of developing an
arithmetical continuum had involved the nature
of "systems".

The nature of identity with respect to the received
paradigm arises from logical atomism and reflects on
the matter in terms of "self-identity", an ontological
necessity. However, identity with respect to a system
involves "identity and difference" (Heidegger's title).

My book in relation algebras attributes the observation
that every system has 4 necessary relations:

The total relation consists of all ordered pairs.

The empty relation consists of no ordered pairs.

The identity relation consists of ordered pairs
whose relata are co-referring names.

The diversity relation consists of ordered pairs
whose relata are never co-referring names.


The identity and diversity relations are logical
complements. So, in relation to systems one has
"identity", "negation", and "totality" intermingled
before one ever states that about which one is
speaking.

Brouwer, thinking of the classical syllogistic
hierarchy, introduced the notion of a pre-linguistic
mathematician precisely because he saw the "part"
relation of syllogistic logic as imposing itself
upon mathematics in foundational pursuits. But, he
overlooks the fact that the continuum can be perceived
as a system of co-extensive parts (Leibniz makes that
exact statement, for one). One of the things that
distinguishes the modern logic from the classical
Aristotelian forms is that it can refer to parts of
objects as individuals. So while there are phiosophical
differences between Cantor's "finished classes" and
Frege's "extensions of concepts", there had been
a convergence among lines of reasoning leading up
to the situation in the foundations of mathematics.

It is a shame that the only reason you seem to have
done your researches had been to discredit the notion
of infinity as it is used in mathematics. Had you
not pursued these histories with an agenda, you may
have had a greater appreciation for how modern
mathematics came to have the form that it does.

[WM]

On 26 Mai, 14:52, fom <fomJ...@nyms.net> wrote:

> The "finished set" is a term that Cantor introduced

The "finished or completed infinite set", to be precise. Yes Cantor
introduced it. And that was in question.

> distinguish arbitrary totalities from the inconsistent
> multiplicities that could not be formed.

Finished infinity is inconsistent and cannot be formed as, for
instance matheology § 271 tomorrow will show (and like everybody could
immediately obtain from the word).

> It is a shame that the only reason you seem to have
> done your researches had been to discredit the notion
> of infinity as it is used in mathematics.

The notion of actual infinity has never been used in mathematics. It
is purest matheology, leading to thoughts that nobody can think and to
absolute insane and useless ideas like inaccessible cardinals. I would
not hinder anybody to pursue that mess. But it is really a shame that
that nonsense it paid by guileless taxpayers.

Regards, WM

[fom]

Your last statement applies to a great many
things arising from "ivory towers".

I have mixed feelings about the relation
of government subsidy and educational/research
practices of universities. Each country has
its own approaches. The U.S. seems to have a
shell game which impoverishes students for the
sake of institutional prestige. To the extent
that I have watched these developments, I have
viewed the phrase "greater good" (as is often
used in educational and governmental contexts)
with deeper and deeper cynicism. I do realize
that such a situation is probably a matter of the
human condition. Every now and then a "cultural
revolution" takes place in response to such
excesses.

It is almost Hegelian.

[Newberry]

The conclusions of transfinite set theory have no practical application IN PRINCIPLE - there cannot possibly be any.

We are supposedly living in the scientific age and mathematics is the queen of sciences. Yet the mathematicians discarded the verification principle, the pragmatic principle and Occam's razor. They rave how "powerful" the axiom of choice is although it has absolutely no practical consequences. They developed a vast, empty structure far worse than Aristotelian metaphysics. Literally meaningless marks on paper. This is scandalous. Cantor/Zermelo set theory will go on the dustbin of history.

[Sam Sung]

fom wrote:

> It is almost Hegelian.

Idiot WM is just Assholian, nothing else - and the idiot WM coverts
these who cannot stop to "discuss" his assholian crap into other idiots.

[Sam Sung]

> fom wrote:
>
>> It is almost Hegelian.
>
> Idiot WM is just Assholian, nothing else - and the idiot WM

converts or turns

[Virgil]

In article
<66361d6d-e360-4c22...@g7g2000vbv.googlegroups.com>,

But once that cat was let out of the bag, not eve WM can put it back in.
--

[Virgil]

In article
<964855e6-9737-4b0d...@dl10g2000vbb.googlegroups.com>,

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

> On 26 Mai, 10:19, Sam Sung <n...@mail.invalid> wrote:
> > Idiot WM babbles:
> >
> > > On 25 Mai, 22:45, Virgil <vir...@ligriv.com> wrote:
> >
> > >> Cantor has two totally different proofs showing why the set of real
> > >> numbers cannot be covered by any listing of its members,
> >
> > > Of course that is true. Had he not uttered the weird idea that
> > > infinite sets could be finished and completely listed, nobody would
> > > care.
> >
> > Cantor did not state that infinite sets "could be finished".
>
> How should omega + 1 > omega, if omega was not finished?

How should 1 + omega = omega if omega was not infinite?
--

[Virgil]

In article
<8cf1f9c0-a467-4de1...@bz1g2000vbb.googlegroups.com>,

That WM is being paid by guileless taxpayers is a far greater shame.
--

[Virgil]

In article
<8fa497c0-b6d5-493b...@y5g2000vbg.googlegroups.com>,

Mathematics outside of WMytheology is quite satisfied with "every n" and
does not, like WM, claim any need for more.

Mathematics outside of WMytheology can deal quite easily with both
"for every n in |N" and "for all n in |N" which WM admits he cannot.
--

[fom]

On 5/26/2013 10:53 AM, Newberry wrote:
>
> The conclusions of transfinite set theory have no practical application IN PRINCIPLE - there cannot possibly be any.
>
> We are supposedly living in the scientific age and mathematics is the queen of sciences. Yet the mathematicians discarded the verification principle, the pragmatic principle and Occam's razor. They rave how "powerful" the axiom of choice is although it has absolutely no practical consequences. They developed a vast, empty structure far worse than Aristotelian metaphysics. Literally meaningless marks on paper. This is scandalous. Cantor/Zermelo set theory will go on the dustbin of history.
>

It seems strange that an off-topic
comment to WM should have attracted
the attention it did.

Well, your comment here exposes
the insincerity of your other posts.

You wish to invoke Strawsonian views
in order to introduce a semantics involving
truth value gaps. Your interests, however,
have nothing to do with Strawson's
contributions.

Strawsonian truth value gap theory arises
from description theory and its relation
to presupposition failures. Instead of
whining about verification principles, why
don't you show us how to make the logic
that involves those questions appropriate
for mathematical purposes?

http://plato.stanford.edu/entries/logic-free/

As for what will end up on the dustbin of
history, I have little doubt that you are
correct. It will not, however, happen for
the reasons you choose to believe.

[fom]

On 5/26/2013 8:59 AM, WM wrote:
>

> The notion of actual infinity has never been used in mathematics.
>

Let me concede this statement for the sake of
argument.

I do so to encourage you to learn more about
Kant and Frege. In his dissertation paper,

http://johnmacfarlane.net/dissertation.pdf

MacFarlane attributes certain specific notions
of logic as an independent discipline to Kant.
Then he discusses Frege's efforts in relation
to logic. Since I read the whole paper, I am
uncertain if the sections on Kant and Frege
(4 and 5) can be read independently.

What I hope to convey here is actually obscured
somewhat in MacFarlane's paper. The kind of
abstract "general logic" associated with modern
axiomatic mathematics is discussed by MacFarlane.
But, MacFarlane ignores Kant's "transcendental
logic". It is this fragment of Kant's work that
translates to set-theoretic principles. Kant does
not call it "mathematics".

Along similar lines, you might find Andrej Bauer's
response in the following link of interest,

http://mathoverflow.net/questions/127889/is-rigour-just-a-ritual-that-most-mathematicians-wish-to-get-rid-of-if-they-could

He full argument is not supportive of your positions,
but he does discuss the preference for numerical
methods over "logic" that is evident within many
mathematical communities.

Whereas I am inclined to demand that "a little infinity"
is "infinity" and reject minimalizing predicativist
philosophies that I read from time to time, Bauer's
statements reflect, in my opinion, why some mathematicians
are willing to accept "God's gift" of the natural numbers
as urelements.

[Newberry]

On Sunday, May 26, 2013 12:29:48 PM UTC-7, fom wrote:
> On 5/26/2013 10:53 AM, Newberry wrote:
>
> >
>
> > The conclusions of transfinite set theory have no practical application IN PRINCIPLE - there cannot possibly be any.
>
> >
>
> > We are supposedly living in the scientific age and mathematics is the queen of sciences. Yet the mathematicians discarded the verification principle, the pragmatic principle and Occam's razor. They rave how "powerful" the axiom of choice is although it has absolutely no practical consequences. They developed a vast, empty structure far worse than Aristotelian metaphysics. Literally meaningless marks on paper. This is scandalous. Cantor/Zermelo set theory will go on the dustbin of history.
>
> >
>
>
>
> It seems strange that an off-topic
>
> comment to WM should have attracted
>
> the attention it did.
>
>
>
> Well, your comment here exposes
>
> the insincerity of your other posts.

??

>
>
>
> You wish to invoke Strawsonian views
>
> in order to introduce a semantics involving
>
> truth value gaps. Your interests, however,
>
> have nothing to do with Strawson's
>
> contributions.

Well they do; Strawson's logic is the perfect vehicle for it. Actually I arrived at Strawson's logic independently, perhaps through a slightly different route.

>
>
>
> Strawsonian truth value gap theory arises
>
> from description theory and its relation
>
> to presupposition failures.

Well, I re-interpreted Strawson, and I wrote a paper about it too.

> Instead of
>
> whining about verification principles, why
>
> don't you show us how to make the logic
>
> that involves those questions appropriate
>
> for mathematical purposes?

I already did about 10x
http://www.scribd.com/doc/63283823/Formal-Semantics-for-The-Logic-of-Presuppositions
I would like somebody to tell me what is wrong with it.

>
>
>
> http://plato.stanford.edu/entries/logic-free/
>
>
>
> As for what will end up on the dustbin of
>
> history, I have little doubt that you are
>
> correct. It will not, however, happen for
>
> the reasons you choose to believe.

And what do you think those reasons will be?

[WM]

On 26 Mai, 17:53, Newberry <newberr...@gmail.com> wrote:
> On Sunday, May 26, 2013 7:30:30 AM UTC-7, fom wrote:
> > On 5/26/2013 8:59 AM, WM wrote:

> > > The notion of actual infinity has never been used in mathematics. It
>
> > > is purest matheology, leading to thoughts that nobody can think and to
>
> > > absolute insane and useless ideas like inaccessible cardinals. I would
>
> > > not hinder anybody to pursue that mess. But it is really a shame that
>
> > > that nonsense it paid by guileless taxpayers.
>
> > Your last statement applies to a great many
>
> > things arising from "ivory towers".

Nothing that I know of is so blatantly false as finished infinity.
Even astrology is a solid science compared with set theory.

>
> > I have mixed feelings about the relation
>
> > of government subsidy and educational/research
>
> > practices of universities.  Each country has
>
> > its own approaches.  The U.S. seems to have a
>
> > shell game which impoverishes students for the
>
> > sake of institutional prestige.  To the extent
>
> > that I have watched these developments, I have
>
> > viewed the phrase "greater good" (as is often
>
> > used in educational and governmental contexts)
>
> > with deeper and deeper cynicism.  I do realize
>
> > that such a situation is probably a matter of the
>
> > human condition.  Every now and then a "cultural
>
> > revolution" takes place in response to such
>
> > excesses.
>
> > It is almost Hegelian.
>
> The conclusions of transfinite set theory have no practical application IN PRINCIPLE - there cannot possibly be any.

Since the logical foundatiopns are self-contradictory.
>
> We are supposedly living in the scientific age and mathematics is the queen of sciences. Yet the mathematicians discarded the verification principle, the pragmatic principle and Occam's razor. They rave how "powerful" the axiom of choice is although it has absolutely no practical consequences. They developed a vast, empty structure far worse than Aristotelian metaphysics. Literally meaningless marks on paper. This is scandalous. Cantor/Zermelo set theory will go on the dustbin of history.-

Yes, it is clearly this intellectual "achievement" that more than any
other idea ridicules the human race - if ever we should have contact
with extraterrestrial intelligences they will have to laugh a lot.

Regards, WM

[WM]

On 26 Mai, 18:53, Virgil <vir...@ligriv.com> wrote:
> In article

> <66361d6d-e360-4c22-b169-b3224b548...@g7g2000vbv.googlegroups.com>,

>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 25 Mai, 22:45, Virgil <vir...@ligriv.com> wrote:
>
> > > Cantor has two totally different proofs showing why the set of real
> > > numbers cannot be covered by any listing of its members,
>
> > Of course that is true. Had he not uttered the weird idea that
> > infinite sets could be finished and completely listed, nobody would
> > care.
>
> But once that cat was let out of the bag, not eve WM can put it back in.

It is not Schrödinger's cat. Cantor's cat is definitely a stillbirth.

Regards, WM

[WM]

On 26 Mai, 18:56, Virgil <vir...@ligriv.com> wrote:
> In article

> <964855e6-9737-4b0d-b545-6591af6e7...@dl10g2000vbb.googlegroups.com>,

>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 26 Mai, 10:19, Sam Sung <n...@mail.invalid> wrote:
> > > Idiot WM babbles:
>
> > > > On 25 Mai, 22:45, Virgil <vir...@ligriv.com> wrote:
>
> > > >> Cantor has two totally different proofs showing why the set of real
> > > >> numbers cannot be covered by any listing of its members,
>
> > > > Of course that is true. Had he not uttered the weird idea that
> > > > infinite sets could be finished and completely listed, nobody would
> > > > care.
>
> > > Cantor did not state that infinite sets "could be finished".
>
> > How should omega + 1 > omega, if omega was not finished?
>
> How should  1 + omega = omega if omega was not infinite?

omega is not a number. Therefore omega + 1 and 1 + omega are as
undefined as the sum of all natural numbers.

Regards, WM

[fom]

On 5/26/2013 3:53 PM, Newberry wrote:
> On Sunday, May 26, 2013 12:29:48 PM UTC-7, fom wrote:
>
> I already did about 10x
> http://www.scribd.com/doc/63283823/Formal-Semantics-for-The-Logic-of-Presuppositions
> I would like somebody to tell me what is wrong with it.
>

I have already conceded that your work may, in
fact, be interesting. If I knew more about the
references used, I might dispute the application
you perceive it to have. But, I have no particular
dispute with your paper as far as it goes.

I do not understand how my post to WM concerning
taxpayer funding of "bright ideas" attracted
an angry remark concerning dustbins of history.
My response reflected consternation at that
remark more than any criticism of your ideas
in the paper.

>>
>>
>>
>> http://plato.stanford.edu/entries/logic-free/
>>
>>
>>
>> As for what will end up on the dustbin of
>>
>> history, I have little doubt that you are
>>
>> correct. It will not, however, happen for
>>
>> the reasons you choose to believe.
>
> And what do you think those reasons will be?
>
>

Psychologists have already documented the apparently
detrimental effect of "multi-tasking" with information
technology at elite universities in the U.S. such as
M.I.T. One may clearly question such studies. So,
there is nothing definitive. But, I suspect that the
simple emphasis of the world's "masters" for a skilled
working class trained in information technology will
be enough to antiquate what people once did with their
own reason -- fantasy or not.

[Newberry]

On Sunday, May 26, 2013 3:17:04 PM UTC-7, fom wrote:
> On 5/26/2013 3:53 PM, Newberry wrote:
>
> > On Sunday, May 26, 2013 12:29:48 PM UTC-7, fom wrote:
>
> >
>
> > I already did about 10x
>
> > http://www.scribd.com/doc/63283823/Formal-Semantics-for-The-Logic-of-Presuppositions
>
> > I would like somebody to tell me what is wrong with it.
>
> >
>
>
>
>
>
> I have already conceded that your work may, in
>
> fact, be interesting. If I knew more about the
>
> references used, I might dispute the application
>
> you perceive it to have. But, I have no particular
>
> dispute with your paper as far as it goes.
>
>
>
> I do not understand how my post to WM concerning
>
> taxpayer funding of "bright ideas" attracted
>
> an angry remark concerning dustbins of history.
>
> My response reflected consternation at that
>
> remark more than any criticism of your ideas
>
> in the paper.

I was commenting more on the usefulness of transfinite set theory than on the politics of education finances.

[Virgil]

In article
<78624f09-8fd4-434a...@k4g2000vba.googlegroups.com>,

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

> > > How should omega + 1 > omega, if omega was not finished?
> >
> > How should  1 + omega = omega if omega was not infinite?
>
> omega is not a number. Therefore omega + 1 and 1 + omega are as
> undefined as the sum of all natural numbers.

Who gave WM the right to determine what may and what may not be called a
number?

According to the Pythagoreans, sqrt(2) was not a number, but it is now,
and so are a lot of things that WM claims are not, including both most
reals and the very number of reals. But mathematics now includes far
more that WMytheology accepts.
--

[Virgil]

In article
<3eb90b92-4c3b-404f...@gw5g2000vbb.googlegroups.com>,

It is alive and well everywhere outside of Wolkenmuekenheim.
--

[Virgil]

In article <yPCdnYSHyqPa8T_M...@giganews.com>,

fom <fom...@nyms.net> wrote:

> On 5/26/2013 8:59 AM, WM wrote:
> >
> > The notion of actual infinity has never been used in mathematics.

If "God created the natural numbers", as WM's hero Kronecker claimed,
then God must have created infinitely many of them as it is easy to see
that no finite set of them can be perfect/complete, and any such a Godly
creation must be.
--

[fom]

delving into serious philosophy now?

:-)

[A Nony Mouse]

In article
<c3d2d490-cd61-4ff7...@g9g2000vbl.googlegroups.com>,

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

> Nothing that I know of is so blatantly false as finished infinity.

A great many of what WM has presented as proofs of various claims, are
far more blatantly false.

Like his oft repeated claim to have a real linear space bijective
mapping from the set of all binary sequences to the set of all paths in
a Complete Infinite Binary Tree.

[Ralf Bader]

WM wrote:

> On 26 Mai, 17:53, Newberry <newberr...@gmail.com> wrote:
>> On Sunday, May 26, 2013 7:30:30 AM UTC-7, fom wrote:
>> > On 5/26/2013 8:59 AM, WM wrote:
>
>> > > The notion of actual infinity has never been used in mathematics. It
>>
>> > > is purest matheology, leading to thoughts that nobody can think and
>> > > to
>>
>> > > absolute insane and useless ideas like inaccessible cardinals. I
>> > > would
>>
>> > > not hinder anybody to pursue that mess. But it is really a shame that
>>
>> > > that nonsense it paid by guileless taxpayers.
>>
>> > Your last statement applies to a great many
>>
>> > things arising from "ivory towers".
>
> Nothing that I know of is so blatantly false as finished infinity.
> Even astrology is a solid science compared with set theory.

Nobody that I know of surpasses you in stupidity.

[WM]

On 27 Mai, 03:53, fom <fomJ...@nyms.net> wrote:
> On 5/26/2013 8:11 PM, Virgil wrote:
>

> > In article <yPCdnYSHyqPa8T_MnZ2dnUVZ_q2dn...@giganews.com>,

> >   fom <fomJ...@nyms.net> wrote:
>
> >> On 5/26/2013 8:59 AM, WM wrote:
>
> >>> The notion of actual infinity has never been used in mathematics.
>
> > If "God created the natural numbers", as WM's hero Kronecker claimed,

I do not subscribe to everything Kronecker said. I guess, he joked,
but I don't know enough of his private feelings towards God.

All we can say in a scientific manner is this: Men created natural
numbers as elements of human discourse. We know from different indo-
germanic languages that the first natural numbers have common roots
that reach back more than 4000 years. The Greek had a myriade = 10000.
Larger numbers became possible with decimal representation, even
larger with exponentiation, even larger with Ackermann's and other
ideas. And that is all that can be said without matheological
blathering about "all natural numbers".

Regards, WM

[Virgil]

In article <vN6dnUCcX_sqIT_M...@giganews.com>,

fom <fom...@nyms.net> wrote:

> On 5/26/2013 8:11 PM, Virgil wrote:
> > In article <yPCdnYSHyqPa8T_M...@giganews.com>,
> > fom <fom...@nyms.net> wrote:
> >
> >> On 5/26/2013 8:59 AM, WM wrote:
> >>>
> >>> The notion of actual infinity has never been used in mathematics.
> >
> > If "God created the natural numbers", as WM's hero Kronecker claimed,
> > then God must have created infinitely many of them as it is easy to see
> > that no finite set of them can be perfect/complete, and any such a Godly
> > creation must be.
> >
>
> delving into serious philosophy now?
>
> :-)

Not really! Just showing WM up for the fraud he is.
--

[Virgil]

In article
<22d6b7db-4f77-4f6b...@bz1g2000vbb.googlegroups.com>,

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

> And that is all that can be said without matheological
> blathering about "all natural numbers".
>
> Regards, WM

If one can speak of any natural numbers one can speak of all of them, as
without being able to distinguish a natural number from something that
is not a natural number we cannot speak of any of them.

At least that is the way things work outside of WMytheology,
--

[WM]

On 27 Mai, 06:40, Ralf Bader <ba...@nefkom.net> wrote:

> Nobody that I know of surpasses you in stupidity.

Nosce te ipsum!

Regards, WM

[Virgil]

In article
<1c6d73ba-fec6-4a98...@g7g2000vbv.googlegroups.com>,

A bit of advice that WM is both far too stupid and far too arrogant to
take himself.
--

[Ralf Bader]

I do. My stupidity exists but is limited to some weaknesses like commenting
your crap. Your stupidity gives a proof of existence of actual infinity
(Dedekind's proof referring to a thought, the thought that one thinks that
thought and so on isn't convincing in its original form. But to be too
stupid about a fact, and to be too stupid to realize that stupidity and so
on ad infinitum is perfectly possible)