Re: Matheology § 269

[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
<111378fd-4e54-4dca...@bh5g2000vbb.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 24 Mai, 20:56, Zeit Geist <tucsond...@me.com> wrote:
> > 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.
>
> 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.

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.
--

[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 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

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

> On 25 Mai, 16:00, Newberry <newberr...@gmail.com> wrote:

> > On Saturday, May 25, 2013 12:14:16 AM UTC-7, WM 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. 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.)
> >
> > I originally misstated it. But anyway this is an interesting point. Does
> > ZFC imply the existence of infinite natural numbers?
>
>
> 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.

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".

[sperm...@yahoo.com]

stop the nonsense it is well known mathematicians even Cantor dont know what a number is-without circularity
thus so much for these proofs about numbers they are meaningless nonsense

All talk about number is meaningless as mathematician dont even know what a number is- without circularity
all their definitions about numbers reduce to just this

a number is a number-circularity impredicative

thus we then dont know what a number is



mathematicians give all these proofs about numbers but they dont even know what a number is so their proofs are worthless
as without knowing what a number is they then cant even IDENTIFY what a number is

Australias lead erotic poet colin leslie dean points out Mathematicians cannot define a number with out being impredicative-ie self referential thus mathematicians dont even know what a number is- thus maths is meaningless All mathematicians can say is a number is a number ?thus they don?t know what a number is thus maths is meaningless

http://www.scribd.com/doc/40697621/Mathematics-Ends-in-Meaninglessness-ie-self-contradiction


http://www.iep.utm.edu/predicat/
http://www.iep.utm.edu/predicat/

In many approaches to the foundations of mathematics, the property N
of being a natural number is defined as follows. An object x has the
property N just in case x has every property F which is had by zero
and is inherited from any number u to its successor u+1. Or in
symbols:
Def-N N(x) ? ?F[F(0) ? ?u(F(u) ? F(u + 1)) ? F(x)]
This definition has the nice feature of entailing the principle of
mathematical induction, which says that any property F which is had by
zero and is inherited from any number u to its successor u+1 is had by
every natural number:
?F{F(0) ? ?u(F(u) ? F(u + 1)) ? ?x(N(x) ? F(x))}
However, Def-N is impredicative because it defines the property N by
generalizing over all arithmetical properties, including the one being
defined.


again impredicative definition
Let n be smallest natural number such that every natural number can be
written as the sum of at most four cubes.
again impredicative definition


http://en.wikipedia.org/wiki/Impredicativity
Concerning mathematics, an example of an impredicative definition is
the smallest number in a set, which is formally defined as: y = min(X)
if and only if for all elements x of X, y is less than or equal to x,
and y is in X.


http://en.wikipedia.org/wiki/Set-theore ... al_numbers
http://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers

A consequence of Kurt Gödel's work on incompleteness is that in any effectively generated axiomatization of number theory (ie. one containing minimal arithmetic), there will be true statements of number theory which cannot be proven in that system. So trivially it follows that ZFC or any other effectively generated formal system cannot capture entirely what a number is.

Whether this is a problem or not depends on whether you were seeking a formal definition of the concept of number. For people such as Bertrand Russell (who thought number theory, and hence mathematics, was a branch of logic and number was something to be defined in terms of formal logic) it was an insurmountable problem. But if you take the concept of number as an absolutely fundamental and irreducible one, it is to be expected. After all, if any concept is to be left formally undefined in mathematics, it might as well be one which everyone understands.

Poincaré, amongst others (Bernays, Wittgenstein), held that any attempt to define natural number as it is endeavoured to do so above is doomed to failure by circularity. Informally, Gödel's theorem shows that a formal axiomatic definition is impossible (incompleteness), Poincaré claims that no definition, formal or informal, is possible (circularity). As such, they give two separate reasons why purported definitions of number must fail to define number. A quote from Poincaré: "The definitions of number are very numerous and of great variety, and I will not attempt to enumerate their names and their authors. We must not be surprised that there are so many. If any of them were satisfactory we should not get any new ones." A quote from Wittgenstein: "This is not a definition. This is nothing but the arithmetical calculus with frills tacked on." A quote from Bernays: "Thus in spite of the possibility of incorporating arithmetic into logistic, arithmetic constitutes the more abstract ('purer') schema; and this appears paradoxical only because of a traditional, but on closer examination unjustified view according to which logical generality is in every respect the highest generality."

[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.

[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 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.

[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

[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.

[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,
--