Mathelogy § 011

WM

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May 18, 2012, 1:44:10 AM5/18/12

to

God knows a list of all natural numbers [*]. In which way does he
memorize the real numbers?

[*] As an example I refer to the totality, the incarnation of all
finite integer positive numbers; this set is a thing by itself and
forms, apart from the natural sequence of the involved numbers, a
fixed and in all parts defined quantum, an aphorismenon, which
obviously must be called larger than every finite number. ... Compare
St. Augustin's concurring perception of the integer sequence as an
actually infinite quantum (De civitate Dei. lib. XII, cap. 19):
Against those who say God could not know infinite things.

Als Beispiel führe ich die Gesamtheit, den Inbegriff aller endlichen
ganzen positiven Zahlen an; diese Menge ist ein Ding für sich und
bildet, ganz abgesehen von der natürlichen Folge der dazu gehörigen
Zahlen, ein in allen Teilen festes, bestimmtes Quantum, ein
aphorismenon, das offenbar größer zu nennen ist als jede endliche
Anzahl. [...] Man vgl. die hiermit übereinstimmende Auffassung der
ganzen Zahlenreihe als aktual-unendliches Quantum bei S. Augustin (De
civitate Dei. lib. XII, cap. 19): Contra eos, qui dicunt ea, quae
infinita sunt, nec Dei posse scientia comprehendi.
http://agios.org.ua/la/index.php/Aurelius_Augustinus._De_Civitate_Dei_Contra_Paganos._Pars_1#LIBER_XII
[Ernst Zermelo (Hrsg.): "Georg Cantor, Gesammelte Abhandlungen
mathematischen und philosophischen Inhalts. Mit erläuternden
Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor -
Dedekind. Nebst einem Lebenslauf Cantors von Adolf Fraenkel." Georg
Olms Verlagsbuchhandlung, Hildesheim (1966) p. 401f]
http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN237853094

Regards, WM

Virgil

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May 18, 2012, 1:47:34 AM5/18/12

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In article
<27c05ba8-ddbb-4a04...@d6g2000vbe.googlegroups.com>,

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

> God knows a list of all natural numbers [*].

Anyone who uses a claimed "God" to justify his mathematics is far more
priest than mathematician.
--

WM

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May 18, 2012, 9:35:59 AM5/18/12

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On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
> In article
> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,

>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > God knows a list of all natural numbers [*].
>
> Anyone who uses a claimed "God" to justify his mathematics is far more
> priest than mathematician.

He is a matheologian, like everybody who claims to be able to well-
order objects of thought that he cannot identify.

Regards, WM

Nam Nguyen

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May 18, 2012, 9:46:05 AM5/18/12

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And a mathematician who claims to know a list of all natural numbers
is who?

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

Virgil

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May 18, 2012, 3:05:48 PM5/18/12

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In article
<ee86c32f-b80f-41bc...@8g2000vbu.googlegroups.com>,

So WM admits he is the origin of matheology.
--

MoeBlee

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May 18, 2012, 3:47:34 PM5/18/12

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On May 18, 2:05 pm, Virgil <vir...@ligriv.com> wrote:

> So WM admits he is the origin of matheology.

WM is more than anything a polemicist. A polemitician.

MoeBlee

WM

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May 18, 2012, 3:52:42 PM5/18/12

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On 18 Mai, 21:05, Virgil <vir...@ligriv.com> wrote:
> In article

> <ee86c32f-b80f-41bc-bb57-de37f39fc...@8g2000vbu.googlegroups.com>,

>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>
> > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > God knows a list of all natural numbers [*].
>
> > > Anyone who uses a claimed "God" to justify his mathematics is far more
> > > priest than mathematician.
>
> > He is a matheologian, like everybody who claims to be able to well-
> > order objects of thought that he cannot identify.
>
> > Regards, WM
>
> So WM admits he is the origin of matheology.
> --

Of course, he, Cantor, who wrote that about St. Augustin. (I am only
the translator. If you don't trust me, read the original (see lower
part of the original posting).)

Regards, WM

Virgil

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May 18, 2012, 4:36:38 PM5/18/12

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In article
<65f54fa9-c55c-4ef7...@eh4g2000vbb.googlegroups.com>,

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

> On 18 Mai, 21:05, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <ee86c32f-b80f-41bc-bb57-de37f39fc...@8g2000vbu.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
> >
> > > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > > God knows a list of all natural numbers [*].
> >
> > > > Anyone who uses a claimed "God" to justify his mathematics is far more
> > > > priest than mathematician.
> >
> > > He is a matheologian, like everybody who claims to be able to well-
> > > order objects of thought that he cannot identify.
> >
> > > Regards, WM
> >
> > So WM admits he is the origin of matheology.
> > --
>
> Of course

.
> Regards, WM
--

William Hughes

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May 18, 2012, 6:12:00 PM5/18/12

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On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
> In article
> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>

> WM <mueck...@rz.fh-augsburg.de> wrote:
> > God knows a list of all natural numbers [*].
>
> Anyone who uses a claimed "God" to justify his mathematics is far more
> priest than mathematician.
> --

Well, the use of the term "God" is harmless. I often talk
about "God's Algorithm" to refer to a desirable but impractical
way to a result. No theism is implied.

The problem here is that "God" is assumed to have no computational
constraints (e.g. God knows the value of Chaitin's omega). As such
it is assumed that God knows which strings are definitions and which
are not. Thus while we know there is no computable list of all
computable
numbers, God knows a definable list of all definable numbers. Noting
that
the anti-diagonal of a definable list is definable, we get a
contradiction.
I suspect this is a complicated way of saying "X is the smallest
natural
that cannot be defined is less than 1000 characters".

WM

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May 18, 2012, 7:19:29 PM5/18/12

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On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote:
> On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
>
> > In article
> > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > God knows a list of all natural numbers [*].
>
> > Anyone who uses a claimed "God" to justify his mathematics is far more
> > priest than mathematician.
> > --
>
> Well, the use of the term "God" is harmless. I often talk
> about "God's Algorithm" to refer to a desirable but impractical
> way to a result. No theism is implied.

But Cantor's finished infinity and list of all reals implies theism.

>
> The problem here is that "God" is assumed to have no computational
> constraints (e.g. God knows the value of Chaitin's omega). As such
> it is assumed that God knows which strings are definitions and which
> are not.

It is funny to see that matheologicans try to circumvent the problem
of existence of only countably many definitions by saying: "We cannot
know which strings are definitions and which are not." The set F of
all finite strings is countable. The set D of definitions is a subset
of F and therefore countable too. Only that's what counts!

> Thus while we know there is no computable list of all
> computable
> numbers, God knows a definable list of all definable numbers. Noting
> that
> the anti-diagonal of a definable list is definable, we get a
> contradiction.

No. Noting that an actually infinite string has no meaning at all, we
see that diagonalization is not a means of mathematics. The whole
problem disappears with the assumtion of completed infinite sets, i.e.
with the assumption of finished infinity or time after never.

Regards, WM

Virgil

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May 18, 2012, 8:25:24 PM5/18/12

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In article
<c76bf82d-cc13-4605...@f30g2000vbz.googlegroups.com>,

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

> On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote:
> > On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
> >
> > > In article
> > > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
> >
> > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > God knows a list of all natural numbers [*].
> >
> > > Anyone who uses a claimed "God" to justify his mathematics is far more
> > > priest than mathematician.
> > > --
> >
> > Well, the use of the term "God" is harmless. I often talk
> > about "God's Algorithm" to refer to a desirable but impractical
> > way to a result. No theism is implied.
>
> But Cantor's finished infinity and list of all reals implies theism.

Not to atheists.

> >
> > The problem here is that "God" is assumed to have no computational
> > constraints (e.g. God knows the value of Chaitin's omega). As such
> > it is assumed that God knows which strings are definitions and which
> > are not.
>
> It is funny to see that matheologicans try to circumvent the problem
> of existence of only countably many definitions by saying: "We cannot
> know which strings are definitions and which are not." The set F of
> all finite strings is countable. The set D of definitions is a subset
> of F and therefore countable too. Only that's what counts!

Honest mathematicians are quite ready to accept that there may be things
out there that are in some sense undefineable, but still there.

The definable things are only the ones we can, at least metaphorically,
get our hands on.

There are more things in Heaven and Earth, Horatio....

>
> > Thus while we know there is no computable list of all
> > computable
> > numbers, God knows a definable list of all definable numbers. Noting
> > that
> > the anti-diagonal of a definable list is definable, we get a
> > contradiction.
>
> No. Noting that an actually infinite string has no meaning at all, we
> see that diagonalization is not a means of mathematics. The whole
> problem disappears with the assumtion of completed infinite sets, i.e.
> with the assumption of finished infinity or time after never.

So that in WM's world one cannot have any mapping f: N -> S, for N being
the set of naturals and S being non-empty because it would require a
finished infinity.

And that will certainly make any sort of real functions impossible as
well.
--

Jesse F. Hughes

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May 18, 2012, 9:27:24 PM5/18/12

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By now, you should be able to tell the difference between the following
two statements:

(1) I can well-order R.

(2) ZFC proves that there is a well-ordering of R.

Surely, (2) is not controversial in the least. If you ever encounter
anyone who claims (1) -- and, when pressed, insists it means something
different than (2) -- why, then, your "argument" might hold some water.

--
"I AM serious about this being a short route to a Ph.d for some of
you, but just remember, I'm the guy who proved Fermat's Last Theorem
in just a bit over 6 years [...] My standards are kind of high."
--James Harris, founding a new mathematical school

Jesse F. Hughes

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May 18, 2012, 11:06:28 PM5/18/12

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

> On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote:
>> On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
>>
>> > In article
>> > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>>
>> > WM <mueck...@rz.fh-augsburg.de> wrote:
>> > > God knows a list of all natural numbers [*].
>>
>> > Anyone who uses a claimed "God" to justify his mathematics is far more
>> > priest than mathematician.
>> > --
>>
>> Well, the use of the term "God" is harmless. I often talk
>> about "God's Algorithm" to refer to a desirable but impractical
>> way to a result. No theism is implied.
>
> But Cantor's finished infinity and list of all reals implies theism.

Right.

Sure it does.

Tell you what. Let's change the subject ever so slightly. Let's talk
about theorems of ZFC. Surely, ZFC doesn't imply theism, does it? If
so, you be sure to tell us how. If not, let's just talk about instead
of that mean ol' Cantor and his gosh-awful "finished infinity".

--
Jesse F. Hughes

"if i'm a loser then who the fuck can even dream they are a winner?"
-- James S. Harris: Tweeter (ret.), non-loser

LudovicoVan

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May 18, 2012, 11:20:36 PM5/18/12

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"WM" <muec...@rz.fh-augsburg.de> wrote in message
news:c76bf82d-cc13-4605-8f26-

> But Cantor's finished infinity and list of all reals implies theism.

In that sense, even the set N is a finished (complete) infinity and implies
some kind of theism. That mathematics needs a philosophy of mathematics is
not, per se, a disease, is it?

-LV

WM

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May 19, 2012, 4:40:07 AM5/19/12

to

On 19 Mai, 02:25, Virgil <vir...@ligriv.com> wrote:

> > It is funny to see that matheologicans try to circumvent the problem
> > of existence of only countably many definitions by saying: "We cannot
> > know which strings are definitions and which are not." The set F of
> > all finite strings is countable. The set D of definitions is a subset
> > of F and therefore countable too. Only that's what counts!
>
> Honest mathematicians are quite ready to accept that there may be things
> out there that are in some sense undefineable, but still there.

No honest mathematician can think so. It is purematheology. Only God
could be "out there".

>
> The definable things are only the ones we can, at least metaphorically,
> get our hands on.
>
> There are more things in Heaven and Earth, Horatio....

Things yes, but not ideas that nobody can have.

>
>
>
> So that in WM's world one cannot have any mapping f: N -> S, for N being
> the set of naturals and S being non-empty because it would require a
> finished infinity.
>
> And that will certainly make any sort of real functions impossible as
> well.

Functions have finite definitions. They were created before infinity
had been considered finished - and they will last after that nonsense
will have broken away.

Regards, WM

WM

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May 19, 2012, 4:53:11 AM5/19/12

to

On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote:
> >> On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
>
> >> > In article
> >> > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>
> >> > WM <mueck...@rz.fh-augsburg.de> wrote:
> >> > > God knows a list of all natural numbers [*].
>
> >> > Anyone who uses a claimed "God" to justify his mathematics is far more
> >> > priest than mathematician.
> >> > --
>
> >> Well, the use of the term "God" is harmless. I often talk
> >> about "God's Algorithm" to refer to a desirable but impractical
> >> way to a result. No theism is implied.
>
> > But Cantor's finished infinity and list of all reals implies theism.
>
> Right.
>
> Sure it does.
>
> Tell you what. Let's change the subject ever so slightly. Let's talk
> about theorems of ZFC.

ZFC: There are countably many rationals and uncountably many
irrationals in (0, 1).

Now cover every rational with an interval, namely the n-th rational
q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
the unit interval with aleph_0 intervals. In the remaining 8/9 (or
more) there are uncountably many irrationals. But every two
irrationals have a rational between each other. That implies in the
present example, they have even a finite interval between each other,
because there are no rationals outside of intervals. So we have
uncountably many irrationals separated by countably many rationals.
Contradiction.

Usually there is some blathering about "Cantor-dust" in the reply. But
even elements of Cantor-dust must be separated by intervals around
rational numbers.

Regards, WM

WM

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May 19, 2012, 4:56:43 AM5/19/12

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On 19 Mai, 05:20, "LudovicoVan" <ju...@diegidio.name> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

>
> news:c76bf82d-cc13-4605-8f26-
>
> > But Cantor's finished infinity and list of all reals implies theism.
>
> In that sense, even the set N is a finished (complete) infinity and implies
> some kind of theism.

Of course. Since Darwin we should do better.

"Platonism is the medieval metaphysics of mathematics; surely we can
do better" [Solomon Feferman, KB 090614]
http://www.hs-augsburg.de/~mueckenh/KB/KB%20001-200.pdf

> That mathematics needs a philosophy of mathematics is
> not, per se, a disease, is it?

A philosophy is good, a religion, for mathematics, is bad.

Regards, WM

WM

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May 19, 2012, 4:44:43 AM5/19/12

to

On 19 Mai, 03:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
> >> In article
> >> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>
> >> WM <mueck...@rz.fh-augsburg.de> wrote:
> >> > God knows a list of all natural numbers [*].
>
> >> Anyone who uses a claimed "God" to justify his mathematics is far more
> >> priest than mathematician.
>
> > He is a matheologian, like everybody who claims to be able to well-
> > order objects of thought that he cannot identify.
>
> By now, you should be able to tell the difference between the following
> two statements:
>
> (1) I can well-order R.

That is Zermelo's claim: Every set can be well ordered.

>
> (2) ZFC proves that there is a well-ordering of R.

That implies matheology: No man can do it. But it can be done or has
been done. How and by whom?

>
> Surely, (2) is not controversial in the least.

Surely (2) is pure nonsense. Objects can exist without names. Names
cannot exists without names. Numbers are names or definitions.
Undefinable definitions are humbug.

> If you ever encounter
> anyone who claims (1)

Zermelo did so. In German "Beweis, dass jede Menge wohlgeordnet werden
kann" means "it can be done".

Regards, WM

Jesse F. Hughes

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May 19, 2012, 7:31:38 AM5/19/12

to

Well, so much for talking about theorems of ZFC, eh?

> Usually there is some blathering about "Cantor-dust" in the reply. But
> even elements of Cantor-dust must be separated by intervals around
> rational numbers.

Quite right. You've proved ZFC is inconsistent and them mean ol'
mathematicians ignore you. My, oh my!

--
"I told her that I loved her.
She said she loved me too.
Neither one was lying,
Yet it wasn't true." -- Del McCoury Band

WM

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May 19, 2012, 7:56:58 AM5/19/12

to

On 19 Mai, 13:31, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> >> Let's talk
> >> about theorems of ZFC.
>
> > ZFC: There are countably many rationals and uncountably many
> > irrationals in (0, 1).
>
> > Now cover every rational with an interval, namely the n-th rational
> > q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
> > the unit interval with aleph_0 intervals. In the remaining 8/9 (or
> > more) there are uncountably many irrationals. But every two
> > irrationals have a rational between each other. That implies in the
> > present example, they have even a finite interval between each other,
> > because there are no rationals outside of intervals. So we have
> > uncountably many irrationals separated by countably many rationals.
> > Contradiction.
>
> Well, so much for talking about theorems of ZFC, eh?

I knew you would not talk to the topic - as usual when your "logic" is
exhausted. But perhaps other read it and wonder how that could be.

>
> > Usually there is some blathering about "Cantor-dust" in the reply. But
> > even elements of Cantor-dust must be separated by intervals around
> > rational numbers.
>
> Quite right. You've proved ZFC is inconsistent and them mean ol'
> mathematicians ignore you.

You are in gross error. *Matheologicans* must ignore that because they
cannot refute it and they cannot accept it either without losing their
ideology and, in many cases, their occupation. Mathematicians know:
Every sentence that starts with the phrase "For all natural numbers"
is false.

Regards, WM

Jesse F. Hughes

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May 19, 2012, 7:54:50 AM5/19/12

to

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

> On 19 Mai, 03:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
>> >> In article
>> >> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>>
>> >> WM <mueck...@rz.fh-augsburg.de> wrote:
>> >> > God knows a list of all natural numbers [*].
>>
>> >> Anyone who uses a claimed "God" to justify his mathematics is far more
>> >> priest than mathematician.
>>
>> > He is a matheologian, like everybody who claims to be able to well-
>> > order objects of thought that he cannot identify.
>>
>> By now, you should be able to tell the difference between the following
>> two statements:
>>
>> (1) I can well-order R.
>
> That is Zermelo's claim: Every set can be well ordered.

As a theorem in ZFC, it is stated something like this:

There is a relation <_R on R such that <_R is a well-ordering.

Mathematical theorems are not really about "doing".

>> (2) ZFC proves that there is a well-ordering of R.
>
> That implies matheology: No man can do it. But it can be done or has
> been done. How and by whom?

A nonsensical question!

>>
>> Surely, (2) is not controversial in the least.
>
> Surely (2) is pure nonsense. Objects can exist without names. Names
> cannot exists without names. Numbers are names or definitions.
> Undefinable definitions are humbug.

And a silly response! If you know what a well-ordering is, then you can
see that it makes no mention of names at all. Similarly, membership in
the set R has nothing to do with being "named".

>> If you ever encounter
>> anyone who claims (1)
>
> Zermelo did so. In German "Beweis, dass jede Menge wohlgeordnet werden
> kann" means "it can be done".

Whatever Zermelo's original expression was, it's perfectly clear what a
mathematician means when he says that there is a well-ordering on R.

I suppose that you can take solace in the following .sig serendipity.

--
"I don't know anything[...] I'm one of the intellectuals."
"That means you got brains."
"Yeah, brains without purpose. Noise without sound. Shape without
substance." -- The Petrified Forest (1936)

YBM

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May 19, 2012, 8:00:18 AM5/19/12

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Le 19.05.2012 13:56, WM a �crit :

Every post finishing by "Regards, WM" is a full of crap.

WM

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May 19, 2012, 8:14:13 AM5/19/12

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On 19 Mai, 13:54, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 19 Mai, 03:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> >> WM <mueck...@rz.fh-augsburg.de> writes:
> >> > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
> >> >> In article
> >> >> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>
> >> >> WM <mueck...@rz.fh-augsburg.de> wrote:
> >> >> > God knows a list of all natural numbers [*].
>
> >> >> Anyone who uses a claimed "God" to justify his mathematics is far more
> >> >> priest than mathematician.
>
> >> > He is a matheologian, like everybody who claims to be able to well-
> >> > order objects of thought that he cannot identify.
>
> >> By now, you should be able to tell the difference between the following
> >> two statements:
>
> >> (1) I can well-order R.
>
> > That is Zermelo's claim: Every set can be well ordered.
>
> As a theorem in ZFC, it is stated something like this:
>
> There is a relation <_R on R such that <_R is a well-ordering.

Of course meanwhile the formulations have been done more carefully.
Concrete claims can be refuted too easily.

But Zermelo did not claim that there is a we-ll-ordred set that
contains all real numbers or that there exists a well-ordering of R,
but he "proved" that every set including R can become well-ordered. In
his proof he presupposed well-order already:
"If m' was the first element that ..."
That means he assumed the existence of a first element of the
remaining set - in his proof that every non empty subset contains a
first element!!!

So assuming, that every non empty subset contains a first element, he
proved that every non empty subset contains a first element.

>
> Mathematical theorems are not really about "doing".

Don't mix up mathematics and matheology, please.

>
> >> (2) ZFC proves that there is a well-ordering of R.
>
> > That implies matheology: No man can do it. But it can be done or has
> > been done. How and by whom?
>
> A nonsensical question!

I believe you that you honestly are incapable of understanding.

>
>
> > Numbers are names or definitions.
> > Undefinable definitions are humbug.
>
> And a silly response! If you know what a well-ordering is, then you can
> see that it makes no mention of names at all.

It mentions first elements. Elements of a set necessarily must be
distinct. Otherwise there could be many first elements.

> Similarly, membership in
> the set R has nothing to do with being "named".

You accept two or more elements that you cannot distinguish? That's
matheology. God can distinguish everything.

Regards, WM

WM

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May 19, 2012, 8:15:51 AM5/19/12

to

> Every post finishing by "Regards, WM" is a full of crap.- Zitierten Text ausblenden -
>
> - Zitierten Text anzeigen -

Even in case I annoy you, I will not stop to be polite.

Regards, WM

Jesse F. Hughes

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May 19, 2012, 8:35:38 AM5/19/12

to

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

> On 19 Mai, 13:31, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> >> Let's talk
>> >> about theorems of ZFC.
>>
>> > ZFC: There are countably many rationals and uncountably many
>> > irrationals in (0, 1).
>>
>> > Now cover every rational with an interval, namely the n-th rational
>> > q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
>> > the unit interval with aleph_0 intervals. In the remaining 8/9 (or
>> > more) there are uncountably many irrationals. But every two
>> > irrationals have a rational between each other. That implies in the
>> > present example, they have even a finite interval between each other,
>> > because there are no rationals outside of intervals. So we have
>> > uncountably many irrationals separated by countably many rationals.
>> > Contradiction.
>>
>> Well, so much for talking about theorems of ZFC, eh?
>
> I knew you would not talk to the topic - as usual when your "logic" is
> exhausted. But perhaps other read it and wonder how that could be.

Perhaps.

But, as far as I am concerned, the fact is that you've failed to present
a coherent argument which supports your conclusion. I simply cannot
follow it. Perhaps that is my own fault, but let's allow others to join
in and affirm the clarity and validity of your own argument.

Alternatively, surely you could take the time to present a perfectly
formal argument with the same conclusion, one so clear and unambiguous
that no one could legitimately claim that the conclusion fails to follow
from the premises.

>>
>> > Usually there is some blathering about "Cantor-dust" in the reply. But
>> > even elements of Cantor-dust must be separated by intervals around
>> > rational numbers.
>>
>> Quite right. You've proved ZFC is inconsistent and them mean ol'
>> mathematicians ignore you.
>
> You are in gross error. *Matheologicans* must ignore that because they
> cannot refute it and they cannot accept it either without losing their
> ideology and, in many cases, their occupation. Mathematicians know:
> Every sentence that starts with the phrase "For all natural numbers"
> is false.

Well, I'm just a poor housewife[1], so I reckon I've no clear idea why
that follows. Sentences such as, "Every natural number is either odd or
even" and "Every natural other than zero is a successor" seem perfectly
clear and true to me, but I guess smart ol' mathematicians know better.

How any mathematicians are there, anyway? More than one? Can you name
a second?

Footnotes:
[1] Just to be clear, I am male and use the term in a humorous sense.

--
"Sure, maybe I have a tiresome task that is nearly impossible, but
part of who I am is an endless amount of energy as long as there is
hope. Without hope, I find that I start to lose focus, and feel, just,
well, hopeless." -- James S. Harris

Jesse F. Hughes

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May 19, 2012, 8:39:25 AM5/19/12

to

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

> On 19 Mai, 13:54, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 19 Mai, 03:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> >> WM <mueck...@rz.fh-augsburg.de> writes:
>> >> > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
>> >> >> In article
>> >> >> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
>>
>> >> >> WM <mueck...@rz.fh-augsburg.de> wrote:
>> >> >> > God knows a list of all natural numbers [*].
>>
>> >> >> Anyone who uses a claimed "God" to justify his mathematics is far more
>> >> >> priest than mathematician.
>>
>> >> > He is a matheologian, like everybody who claims to be able to well-
>> >> > order objects of thought that he cannot identify.
>>
>> >> By now, you should be able to tell the difference between the following
>> >> two statements:
>>
>> >> (1) I can well-order R.
>>
>> > That is Zermelo's claim: Every set can be well ordered.
>>
>> As a theorem in ZFC, it is stated something like this:
>>
>> There is a relation <_R on R such that <_R is a well-ordering.
>
> Of course meanwhile the formulations have been done more carefully.
> Concrete claims can be refuted too easily.

Are you suggesting the above claim is not "concrete"?

>
> But Zermelo did not claim that there is a we-ll-ordred set that
> contains all real numbers or that there exists a well-ordering of R,
> but he "proved" that every set including R can become well-ordered. In
> his proof he presupposed well-order already:
> "If m' was the first element that ..."
> That means he assumed the existence of a first element of the
> remaining set - in his proof that every non empty subset contains a
> first element!!!
>
> So assuming, that every non empty subset contains a first element, he
> proved that every non empty subset contains a first element.

I've expressed no opinion on Zermelo's original formulation. Let's talk
about what ZFC proves instead.

>> Mathematical theorems are not really about "doing".
>
> Don't mix up mathematics and matheology, please.

Oh, do fuck off with this silliness. We're talking about mathematical
theorems and their content.

>> >> (2) ZFC proves that there is a well-ordering of R.
>>
>> > That implies matheology: No man can do it. But it can be done or has
>> > been done. How and by whom?
>>
>> A nonsensical question!
>
> I believe you that you honestly are incapable of understanding.

Maybe so!

>> > Numbers are names or definitions.
>> > Undefinable definitions are humbug.
>>
>> And a silly response! If you know what a well-ordering is, then you can
>> see that it makes no mention of names at all.
>
> It mentions first elements. Elements of a set necessarily must be
> distinct. Otherwise there could be many first elements.

Eh, more things I can't understand.

I reckon this conversation is doing neither of us any damned good at
all. Let's leave it here.

--
Jesse F. Hughes
"It's your choice though, if you do not believe in mathematics, in the
importance of its healthiness and correctness, then you can just walk
away now." -- James S Harris, on the Pythagorean Oath

WM

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May 19, 2012, 8:51:32 AM5/19/12

to

You would not be able to follow it. Whatever I did, you would require
that I started at a more basic level. And that would be quite a lot of
work for nothing. (You shoudl know, there are nearly no proofs in
mathematics that are formalized before many readers have understood
it.)

Where should I start?
There are only countably many rationals q_n in the unit interval?
If each one is covered by an interval I_n of measure 10^-n, then there
are at most countably many intervals I_n?
If some part of measure > eps of the unit interval remains uncovered,
then there are at least uncountably many irrationals uncovered?
There are no two irrationals without an interval I_n containing a
rational number q_n between them?
There are no two irrationals without a border of an interval I_n
containing a rational number q_n between them?

Or are you only weak in deriving conclusions?
>
Regards, WM

Jürgen R.

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May 19, 2012, 9:37:13 AM5/19/12

to

"WM" <muec...@rz.fh-augsburg.de> schrieb im Newsbeitrag
news:8547f7e0-5f4f-4d25...@z19g2000vbe.googlegroups.com...

Nonsense. There is nothing wrong with the proof; and it would be
truly amazing if an argument that has been scrutinized by
every mathematician since 1904 contained such a blatant error.

> "If m' was the first element that ..."
> That means he assumed the existence of a first element of the
> remaining set - in his proof that every non empty subset contains a
> first element!!!

Nonsense. He chooses a first element from a well-ordered subset, first
having shown that such subsets exist.

Mückenheim, you are obviously out of your depth here.

karl

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May 19, 2012, 10:05:48 AM5/19/12

to

>>
>> Every post finishing by "Regards, WM" is a full of crap.- Zitierten Text ausblenden -
>>
>> - Zitierten Text anzeigen -
>
> Even in case I annoy you, I will not stop to be polite.
>
> Regards, WM

Your politeness is apparently limited to sci.math. in de.sci.math you always prefer to insult people whcih contradict
you in a
crude and distasetful way as total idiots. We will see how long you stick here to your politeness.

No regards, Karl

WM

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May 19, 2012, 10:57:12 AM5/19/12

to

On 19 Mai, 15:37, Jürgen R. <jurg...@arcor.de> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> schrieb im Newsbeitragnews:8547f7e0-5f4f-4d25-ac2b-

> > But Zermelo did not claim that there is a we-ll-ordred set that
> > contains all real numbers or that there exists a well-ordering of R,
> > but he "proved" that every set including R can become well-ordered. In
> > his proof he presupposed well-order already:
>
> Nonsense. There is nothing wrong with the proof; and it would be
> truly amazing if an argument that has been scrutinized by
> every mathematician since 1904 contained such a blatant error.

Every mathematician may have thought this way. And every
mathematician, who scrutinized it in earlier times, has assumed that
all elements can be distinguished.

>
> > "If m' was the first element that ..."
> > That means he assumed the existence of a first element of the
> > remaining set - in his proof that every non empty subset contains a
> > first element!!!
>
> Nonsense. He chooses a first element from a well-ordered subset, first
> having shown that such subsets exist.

Rennekamp, you should read the original. After some definitions on p.
514 (the first one), Zermelo writes this sentence "If m' was the first
element that ..." when beginning p. 515. Before that he has only
considered a set of two elements. The "proof" ends with p. 516. And
obviously Zermelo takes for granted that every element can be
addressed, i.e., is defined.

Regards, WM

WM

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May 19, 2012, 11:02:14 AM5/19/12

to

On 19 Mai, 14:39, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 19 Mai, 13:54, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> >> There is a relation <_R on R such that <_R is a well-ordering.
>
> > Of course meanwhile the formulations have been done more carefully.
> > Concrete claims can be refuted too easily.
>
> Are you suggesting the above claim is not "concrete"?

Of course. "There is" is not a concrete expression. Where is? And what
can we do with this being?

>
> I've expressed no opinion on Zermelo's original formulation.

But Zermelo has. And every student who is introduced in this kind of
matheology is told that "there is" a well-order of R. In fact, "there
is" none - for all "theres" that are accessible.
>
Regards, WM

WM

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May 19, 2012, 11:33:39 AM5/19/12

to

On 19 Mai, 16:05, karl <oud...@nononet.com> wrote:
> >> Every post finishing by "Regards, WM" is a full of crap.- Zitierten Text ausblenden -
>
> >> - Zitierten Text anzeigen -
>
> > Even in case I annoy you, I will not stop to be polite.
>
> > Regards, WM
>
> Your politeness is apparently limited to sci.math. in de.sci.math you always prefer to insult people whcih contradict
> you

Who did so?

> in a
> crude and distasetful way as total idiots.

Where did you read that written from my hand?

Don't quote stackexchange. Their a gang of criminal subjects has
abused my name for texts that I did not write.

Regards, WM

Jesse F. Hughes

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May 19, 2012, 1:35:22 PM5/19/12

to

Well, I reckon so.

--
"If you people knew really, in your heats [sic], and minds, who I
actually am, would you even reply to my posts? I'd probably get that
hero worship crap." -- JSH explains why the greatest mathematician
in the world masquerades as a moron.

Jesse F. Hughes

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May 19, 2012, 1:37:16 PM5/19/12

If numbers were merely names, then one number could only be one name,
but any particular number tends to have lots of names.
That is as obvious as 2 + 2 = 4.
>
> >�If you ever encounter

> > anyone who claims (1)
>
> Zermelo did so. In German "Beweis, dass jede Menge wohlgeordnet werden
> kann" means "it can be done".

To claim that something can be done, or even that one has done it, is
merely a claim until it has been seen to have been done.

Consider, for example, Fermat's last "theorem".
Fermat claimed to have a proof for it, but did he really have one?
The proof that was finally found by Andrew Wiles would have been
impossible for Fermat to have found.
--

Virgil

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May 19, 2012, 3:42:52 PM5/19/12

to

In article
<8547f7e0-5f4f-4d25...@z19g2000vbe.googlegroups.com>,

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

> On 19 Mai, 13:54, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 19 Mai, 03:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > >> WM <mueck...@rz.fh-augsburg.de> writes:
> > >> > On 18 Mai, 07:47, Virgil <vir...@ligriv.com> wrote:
> > >> >> In article
> > >> >> <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
> >
> > >> >> WM <mueck...@rz.fh-augsburg.de> wrote:
> > >> >> > God knows a list of all natural numbers [*].
> >
> > >> >> Anyone who uses a claimed "God" to justify his mathematics is far more
> > >> >> priest than mathematician.
> >
> > >> > He is a matheologian, like everybody who claims to be able to well-
> > >> > order objects of thought that he cannot identify.
> >
> > >> By now, you should be able to tell the difference between the following
> > >> two statements:
> >
> > >> (1) I can well-order R.
> >
> > > That is Zermelo's claim: Every set can be well ordered.

To claim that every set can be well ordered it not at all the same as
claiming that one is oneself able to produce such a well-ordering.

>
> Don't mix up mathematics and matheology, please.

Why not, when you do it all the time?

> >
> > >> (2) ZFC proves that there is a well-ordering of R.
> >
> > > That implies matheology: No man can do it. But it can be done or has
> > > been done. How and by whom?
> >
> > A nonsensical question!
>
> I believe you that you honestly are incapable of understanding.

My feeling exactly!

>
> >
> >
> > > Numbers are names or definitions.
> > > Undefinable definitions are humbug.
> >
> > And a silly response! If you know what a well-ordering is, then you can
> > see that it makes no mention of names at all.
>
> It mentions first elements. Elements of a set necessarily must be
> distinct. Otherwise there could be many first elements.
>
> > Similarly, membership in
> > the set R has nothing to do with being "named".
>
> You accept two or more elements that you cannot distinguish? That's
> matheology. God can distinguish everything.

But there is no objective physical evidence that any gods of any sort
exist!
So that the word "god" means the very sort of thing that WM claims is
nonsense.
--

Virgil

unread,

May 19, 2012, 3:45:41 PM5/19/12

to

In article
<a2f7cf4b-be3c-4a81...@dg7g2000vbb.googlegroups.com>,

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

> On 19 Mai, 15:37, Jürgen R. <jurg...@arcor.de> wrote:
> > "WM" <mueck...@rz.fh-augsburg.de> schrieb im
> > Newsbeitragnews:8547f7e0-5f4f-4d25-ac2b-
> > > But Zermelo did not claim that there is a we-ll-ordred set that
> > > contains all real numbers or that there exists a well-ordering of R,
> > > but he "proved" that every set including R can become well-ordered. In
> > > his proof he presupposed well-order already:
> >
> > Nonsense. There is nothing wrong with the proof; and it would be
> > truly amazing if an argument that has been scrutinized by
> > every mathematician since 1904 contained such a blatant error.
>
> Every mathematician may have thought this way. And every
> mathematician, who scrutinized it in earlier times, has assumed that
> all elements can be distinguished.

So are you assuming that there are elements that cannot be distinguished?
--

Virgil

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May 19, 2012, 3:48:22 PM5/19/12

to

In article
<ce499ff1-c4c5-40b7...@e20g2000vbm.googlegroups.com>,

At least those accessible to WM.

So which sets accessible to WM are, at least according to WM, not
well-orderable?
--

WM

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May 19, 2012, 3:51:23 PM5/19/12

to

On 19 Mai, 20:13, karl <oud...@nononet.com> wrote:

> >> in de.sci.math you always prefer to insult people whcih contradict

> >> you in a

> >> crude and distasetful way as total idiots.
>
> > Where did you read that written from my hand?

> I have read your posts in de.sci.math and you are very insulting there.

So it appears as if you accused me falsely. But instead of offering an
apology, you continue with your insults and prefer to be an inveterate
liar.

Typical behaviour of members of the intellectual lower stratum. You
should try to avoid such exhibitions.

Regards, WM

WM

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May 19, 2012, 3:57:31 PM5/19/12

to

On 19 Mai, 21:26, Virgil <vir...@ligriv.com> wrote:
> > > There are more things in Heaven and Earth, Horatio....
>
> > Things yes, but not ideas that nobody can have.
>
> Ideas are not things?

No. Ideas need things in oreder to exist, namely brains or memeories.
Without a brain or memory, ideas cannot be anywhere.

>
> How can one define functions having domains and ranges

Read Euler, Gauss, Cauchy, Weierstrass. There you can learn what a
function is and how it functions (and why it carries that name).

Regards, WM

Virgil

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May 19, 2012, 4:15:47 PM5/19/12

to

In article
<5a80b4c9-a47b-4d93...@hq4g2000vbb.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:

> > > On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote:

> > >> On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
> >
> > >> > In article
> > >> > <27c05ba8-ddbb-4a04-b7c4-fbf16ee94...@d6g2000vbe.googlegroups.com>,
> >
> > >> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > >> > > God knows a list of all natural numbers [*].
> >
> > >> > Anyone who uses a claimed "God" to justify his mathematics is far more
> > >> > priest than mathematician.

> > >> > --
> >
> > >> Well, the use of the term "God" is harmless. I often talk
> > >> about "God's Algorithm" to refer to a desirable but impractical
> > >> way to a result. No theism is implied.
> >

> > > But Cantor's finished infinity and list of all reals implies theism.
> >

> > Right.
> >
> > Sure it does.
> >
> > Tell you what. Let's change the subject ever so slightly. Let's talk

> > about theorems of ZFC.
>
> ZFC: There are countably many rationals and uncountably many
> irrationals in (0, 1).
>
> Now cover every rational with an interval, namely the n-th rational
> q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
> the unit interval with aleph_0 intervals. In the remaining 8/9 (or
> more) there are uncountably many irrationals. But every two
> irrationals have a rational between each other. That implies in the
> present example, they have even a finite interval between each other,
> because there are no rationals outside of intervals. So we have
> uncountably many irrationals separated by countably many rationals.
> Contradiction.

Nope! The contradiction vanishes when one looks closer.

Note that every single irrational is separated from every other
irrational by countably many rationals, at least one of which has one of
your 10^-n intervals strictly between those irrationals.

Let x and y, with x < y be two irrationals in (0,1) the the interval
(x,y) has midpoint m = (x + y)/2 and radius r = (y-x)/2.

Then the interval (m - r/2, m + r/2) is distance r/2 from each of x and
y and , being open, contains infinitely many rational points and thus
contains some rational point q_n with 10^-n < r/2.

Thus proving that, without any contradictions, one will have between any
two irrationals one of those rational intervals , q_n, without any of
the cotradictions alleged by WM.

An WM is, as usual, wrong again! His alleged contradiction certainly
does not exist in mathematics, but only in his own matheology.
--

WM

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May 19, 2012, 4:15:52 PM5/19/12

to

On 19 Mai, 21:45, Virgil <vir...@ligriv.com> wrote:
> In article

> <a2f7cf4b-be3c-4a81-898d-789ed6c3f...@dg7g2000vbb.googlegroups.com>,

If there were uncountably many reals but only countably many
definitions of real, then, yes, then there would be numbers that are
not numbers.

Regards, WM

WM

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May 19, 2012, 4:07:58 PM5/19/12

to

On 19 Mai, 21:34, Virgil <vir...@ligriv.com> wrote:
> In article

> <7e2cd544-cc9d-4bf9-931a-15076a75c...@w13g2000vbc.googlegroups.com>,

And the proof that Zermelo pretended to have found is impossible for
everybody (if R was in fact uncountable) because nobody can well-order
what he cannot distinguish. The set of all distinguishable elements is
a superset of the set of all well-ordered elements. Most logicians
recognize that. Therefore most logicians do not accept that there are
only countably many names. Instead they try with uncountable languages
and related nonsense to maintain that every real number can be namend.
See for instance Andreas Blass in Matheology § 013.

Regards, WM

Virgil

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May 19, 2012, 4:24:57 PM5/19/12

to

In article
<47b0b804-0605-472d...@ec4g2000vbb.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 19 Mai, 13:31, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:

> > > On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > >> Let's talk
> > >> about theorems of ZFC.
> >
> > > ZFC: There are countably many rationals and uncountably many
> > > irrationals in (0, 1).
> >
> > > Now cover every rational with an interval, namely the n-th rational
> > > q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
> > > the unit interval with aleph_0 intervals. In the remaining 8/9 (or
> > > more) there are uncountably many irrationals. But every two
> > > irrationals have a rational between each other. That implies in the
> > > present example, they have even a finite interval between each other,
> > > because there are no rationals outside of intervals. So we have
> > > uncountably many irrationals separated by countably many rationals.
> > > Contradiction

Nope! That alleged contradiction vanishes when one looks closer:

Every single irrational is separated from every other

irrational by countably many rationals, at least one of which has one of
your 10^-n intervals strictly between those irrationals.

Proof:

Let a and b, with a < b be two irrationals in (0,1).
The the interval (a,b) has midpoint m = (a+b)/2 and radius r = (b-a)/2.

Then the interval (m - r/2, m + r/2) is distance r/2 from both a and
b and ,being of positive length, contains infinitely many rational

points and thus
contains some rational point q_n with 10^-n < r/2.

Thus proving that, without any contradictions, one will have between any

two irrationals one of WM�s rational intervals, q_n, without any of
the contradictions alleged by WM.

An WM is, as usual, wrong again! His alleged contradiction certainly
does not exist in mathematics, but only in his own matheology.

> >

> > Well, so much for talking about theorems of ZFC, eh?
>
> I knew you would not talk to the topic - as usual when your "logic" is
> exhausted. But perhaps other read it and wonder how that could be.
> >

> > > Usually there is some blathering about "Cantor-dust" in the reply. But
> > > even elements of Cantor-dust must be separated by intervals around
> > > rational numbers.
> >
> > Quite right. �You've proved ZFC is inconsistent and them mean ol'
> > mathematicians ignore you.
>
> You are in gross error. *Matheologicans* must ignore that because they
> cannot refute it and they cannot accept it either without losing their
> ideology and, in many cases, their occupation. Mathematicians know:
> Every sentence that starts with the phrase "For all natural numbers"
> is false.
>

> Regards, WM
--

Virgil

unread,

May 19, 2012, 4:27:34 PM5/19/12

to

In article
<218da3f3-9d4a-421b...@s9g2000vbg.googlegroups.com>,

Not as weak as WM is:

WM's alleged contradiction vanishes when one looks closer.

Every single irrational is separated from every other
irrational by countably many rationals, at least one of which has one of

WM's 10^-n length intervals strictly between those irrationals.

Proof:

Let a and b, with a < b be two irrationals in (0,1).
The the interval (a,b) has midpoint m = (a+b)/2 and radius r = (b-a)/2.

Then the interval (m - r/2, m + r/2) is distance r/2 from both a and
b and ,being of positive length, contains infinitely many rational
points and thus
contains some rational point q_n with 10^-n < r/2.

Thus proving that, without any contradictions, one will have between any

two irrationals one of WMąs rational intervals, q_n, without any of

the contradictions alleged by WM.

An WM is, as usual, wrong again! His alleged contradiction certainly
does not exist in mathematics, but only in his own matheology.

So much for WM's matheology!
--

Virgil

unread,

May 19, 2012, 4:30:01 PM5/19/12

to

In article
<58596e12-aae0-4593...@b26g2000vbt.googlegroups.com>,

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

> On 19 Mai, 14:00, YBM <ybm...@nooos.fr.invalid> wrote:
> > Le 19.05.2012 13:56, WM a crit :
> >
> >
> >
> >
> >
> > > On 19 Mai, 13:31, "Jesse F. Hughes"<je...@phiwumbda.org> wrote:
> > >> WM<mueck...@rz.fh-augsburg.de> writes:
> > >>> On 19 Mai, 05:06, "Jesse F. Hughes"<je...@phiwumbda.org> wrote:
> > >>>> Let's talk
> > >>>> about theorems of ZFC.
> >
> > >>> ZFC: There are countably many rationals and uncountably many
> > >>> irrationals in (0, 1).
> >
> > >>> Now cover every rational with an interval, namely the n-th rational
> > >>> q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
> > >>> the unit interval with aleph_0 intervals. In the remaining 8/9 (or
> > >>> more) there are uncountably many irrationals. But every two
> > >>> irrationals have a rational between each other. That implies in the
> > >>> present example, they have even a finite interval between each other,
> > >>> because there are no rationals outside of intervals. So we have
> > >>> uncountably many irrationals separated by countably many rationals.
> > >>> Contradiction.

False the first time, and false again no matter how often repeated.

Every single irrational is separated from every other
irrational by countably many rationals, at least one of which has one of

your 10^-n intervals strictly between those irrationals.

Proof:

Let a and b, with a < b be two irrationals in (0,1).
The the interval (a,b) has midpoint m = (a+b)/2 and radius r = (b-a)/2.

Then the interval (m - r/2, m + r/2) is distance r/2 from both a and
b and ,being of positive length, contains infinitely many rational
points and thus
contains some rational point q_n with 10^-n < r/2.

Thus proving that, without any contradictions, one will have between any

two irrationals one of WMšs rational intervals, q_n, without any of

the contradictions alleged by WM.

An WM is, as usual, wrong again! His alleged contradiction certainly
does not exist in mathematics, but only in his own matheology.

--

Virgil

unread,

May 19, 2012, 4:33:18 PM5/19/12

to

In article
<b86804dc-d45a-47a1...@dg7g2000vbb.googlegroups.com>,

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

> On 19 Mai, 21:26, Virgil <vir...@ligriv.com> wrote:
> > > > There are more things in Heaven and Earth, Horatio....
> >
> > > Things yes, but not ideas that nobody can have.
> >
> > Ideas are not things?
>
> No. Ideas need things in oreder to exist, namely brains or memeories.
> Without a brain or memory, ideas cannot be anywhere.
>
> >
> > How can one define functions having domains and ranges

Originally reading

" How can one define functions having domains and ranges which do not
exist other than in WM's matheology?"

And as asked unanswered!
--

karl

unread,

May 19, 2012, 4:34:34 PM5/19/12

to

Oh funny, so all your Kalenderblaetter in de.sci.mathematik are not written by you but by somebody else
posing under your name?

WM

unread,

May 19, 2012, 4:26:19 PM5/19/12

to

On 19 Mai, 22:15, Virgil <vir...@ligriv.com> wrote:

> one will have between any
> two irrationals one of those rational intervals , q_n,

I called the intervals I_n. They have a finite measure. They contain
q_n. But cum grano salis you are right!

> An WM is, as usual, wrong again! His alleged contradiction certainly
> does not exist in mathematics,

Unfortunately you have forgotten to mention how countably many
intervals can separate uncountably many irrationals.

Regards, WM

Virgil

unread,

May 19, 2012, 5:55:32 PM5/19/12

to

In article
<b4640e45-7c99-4024...@b26g2000vbt.googlegroups.com>,

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

> Unfortunately you have forgotten to mention how countably many
> intervals can separate uncountably many irrationals.

Since any one rationally end-pointed interval, of which there are just
countably many, separates uncountably many smaller irrationals from
uncountably many larger irrationals, what is the problem?
--

Virgil

unread,

May 19, 2012, 5:58:26 PM5/19/12

to

In article
<5f25a726-bebd-4cd7...@b26g2000vbt.googlegroups.com>,

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

> > > Zermelo did so. In German "Beweis, dass jede Menge wohlgeordnet werden
> > > kann" means "it can be done".
> >
> > To claim that something can be done, or even that one has done it, is
> > merely a claim until it has been seen to have been done.
> >
> > Consider, for example, Fermat's last "theorem".
> > Fermat claimed to have a proof for it, but did he really have one?
> > The proof that was finally found by Andrew Wiles would have been
> > impossible for Fermat to have found.
>
> And the proof that Zermelo pretended to have found is impossible for
> everybody (if R was in fact uncountable) because nobody can well-order
> what he cannot distinguish.

Claimed but not proven.

And claims without proof are uncceptable.
--

Alan Smaill

unread,

May 19, 2012, 6:07:07 PM5/19/12

to

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

> On 19 Mai, 14:35, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 19 Mai, 13:31, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> >> WM <mueck...@rz.fh-augsburg.de> writes:
>> >> > On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> >> >> Let's talk
>> >> >> about theorems of ZFC.
>>
>> >> > ZFC: There are countably many rationals and uncountably many
>> >> > irrationals in (0, 1).
>>
>> >> > Now cover every rational with an interval, namely the n-th rational
>> >> > q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
>> >> > the unit interval with aleph_0 intervals. In the remaining 8/9 (or
>> >> > more) there are uncountably many irrationals. But every two
>> >> > irrationals have a rational between each other. That implies in the
>> >> > present example, they have even a finite interval between each other,
>> >> > because there are no rationals outside of intervals. So we have
>> >> > uncountably many irrationals separated by countably many rationals.
>> >> > Contradiction.
>>

>> >> Well, so much for talking about theorems of ZFC, eh?
>>
>> > I knew you would not talk to the topic - as usual when your "logic" is
>> > exhausted. But perhaps other read it and wonder how that could be.
>>
>> Perhaps.
>>
>> But, as far as I am concerned, the fact is that you've failed to present
>> a coherent argument which supports your conclusion. I simply cannot
>> follow it. Perhaps that is my own fault, but let's allow others to join
>> in and affirm the clarity and validity of your own argument.
>>
>> Alternatively, surely you could take the time to present a perfectly
>> formal argument with the same conclusion, one so clear and unambiguous
>> that no one could legitimately claim that the conclusion fails to follow
>> from the premises.
>
> You would not be able to follow it. Whatever I did, you would require
> that I started at a more basic level. And that would be quite a lot of
> work for nothing. (You shoudl know, there are nearly no proofs in
> mathematics that are formalized before many readers have understood
> it.)

That work would be very worthwhile, if it can be done.
You tell us that the contradictions are glaring, obvious etc.
If you simply spell this out in ZF, the common basis for maths
these days, then this would be a great mathematical breakthrough,
others would have to pay attention, you would get great personal
credit.

Consider Cantor's reaction to Russell's letter showing the
flaw in Cantor's version of set theory.

> Where should I start?
> There are only countably many rationals q_n in the unit interval?
> If each one is covered by an interval I_n of measure 10^-n, then there
> are at most countably many intervals I_n?
> If some part of measure > eps of the unit interval remains uncovered,
> then there are at least uncountably many irrationals uncovered?
> There are no two irrationals without an interval I_n containing a
> rational number q_n between them?
> There are no two irrationals without a border of an interval I_n
> containing a rational number q_n between them?

Fine -- just spell that out in set theory --
several of these are uncontroversial. Of course,
you would need to be a bit more exact --

" If each one is covered by an interval I_n of measure 10^-n, then there
are at most countably many intervals I_n "

for example has different readings, and you'd need to be explicit.

>>
> Regards, WM

--
Alan Smaill

Jürgen R.

unread,

May 19, 2012, 6:27:37 PM5/19/12

to

"WM" <muec...@rz.fh-augsburg.de> schrieb im Newsbeitrag
news:a2f7cf4b-be3c-4a81...@dg7g2000vbb.googlegroups.com...

> On 19 Mai, 15:37, J�rgen R. <jurg...@arcor.de> wrote:
>> "WM" <mueck...@rz.fh-augsburg.de> schrieb im
>> Newsbeitragnews:8547f7e0-5f4f-4d25-ac2b-
>> > But Zermelo did not claim that there is a we-ll-ordred set that
>> > contains all real numbers or that there exists a well-ordering of R,
>> > but he "proved" that every set including R can become well-ordered. In
>> > his proof he presupposed well-order already:
>>
>> Nonsense. There is nothing wrong with the proof; and it would be
>> truly amazing if an argument that has been scrutinized by
>> every mathematician since 1904 contained such a blatant error.
>
> Every mathematician may have thought this way. And every
> mathematician, who scrutinized it in earlier times, has assumed that
> all elements can be distinguished.
>>

>> > "If m' was the first element that ..."
>> > That means he assumed the existence of a first element of the
>> > remaining set - in his proof that every non empty subset contains a
>> > first element!!!
>>
>> Nonsense. He chooses a first element from a well-ordered subset, first
>> having shown that such subsets exist.
>
> Rennekamp, you should read the original. After some definitions on p.
> 514 (the first one), Zermelo writes this sentence "If m' was the first
> element that ..."

He is talking about the first element of a certain subset of a
well-ordered set.

> when beginning p. 515. Before that he has only
> considered a set of two elements.

He demonstrates existence of "gamma-sets" using two
trivial examples. The argument that follows applies to any
two "gamma-sets".

> The "proof" ends with p. 516. And
> obviously Zermelo takes for granted that every element can be
> addressed, i.e., is defined.

No. "Addressing", whatever that might mean, has nothing to do
with the argument. Nor is "addressing" of "elements" a notion
that has a meaning outside of M�ckenhausen.

>
> Regards, WM

dilettante

unread,

May 19, 2012, 6:27:29 PM5/19/12

to

"WM" <muec...@rz.fh-augsburg.de> wrote in message
news:47b0b804-0605-472d...@ec4g2000vbb.googlegroups.com...

>Every sentence that starts with the phrase "For all natural numbers"
>is false.

>Regards, WM

Surely there are countably many such sentences. Are you saying that ALL of
them are false?
And what about the sentences that begin with "Every sentence"? How many of
them are true?

Jesse F. Hughes

unread,

May 19, 2012, 6:41:40 PM5/19/12

to

Alan Smaill <sma...@SPAMinf.ed.ac.uk> writes:

> Consider Cantor's reaction to Russell's letter showing the
> flaw in Cantor's version of set theory.

Er, wasn't that Frege?

--
"Humanity is still a primitive species. I seem to have been born out
of my time, maybe centuries ahead, and I guess I'll just have to get
used to it. In ways, it's not so bad. Mostly it's boring though."
-- James S. Harris has problems beyond you and me.

Alan Smaill

unread,

May 19, 2012, 6:50:25 PM5/19/12

to

"Jesse F. Hughes" <je...@phiwumbda.org> writes:

> Alan Smaill <sma...@SPAMinf.ed.ac.uk> writes:
>
>> Consider Cantor's reaction to Russell's letter showing the
>> flaw in Cantor's version of set theory.
>
> Er, wasn't that Frege?

Er, yes.

--
Alan Smaill

Graham Cooper

unread,

May 20, 2012, 12:32:35 AM5/20/12

to

On May 20, 8:27 am, Jürgen R. <jurg...@arcor.de> wrote:
> > The "proof" ends with p. 516. And
> > obviously Zermelo takes for granted that every element can be
> > addressed, i.e., is defined.
>
> No. "Addressing", whatever that might mean, has nothing to do
> with the argument. Nor is "addressing" of "elements" a notion
> that has a meaning outside of M ckenhausen.
>

There are Specification Languages but you end up programming the
function in a 4GL like Prolog anyway.

Here is a bnf grammar that could enumerate Prolog Horne Clauses.

So to enumerate all *addressable* reals (or their specifications), you
could use a grammar such as this.

Note this encompasses Predicate Calculus.

Courtesy: VTPROLOG, AI EXPERT MAGAZINE
sentence ::- rule | query | command
rule ::- head '.' | head ':-' tail '.'
query ::- '?-' tail '.'
command ::- '@' file_name '.'
head ::- goal
tail ::- goal | goal ',' tail
goal ::- constant | variable | structure
constant ::- {quoted string} | {token beginning with 'a' .. 'z'}
variable ::- {identifier beginning with 'A' .. 'Z' or '_' }
structure ::- functor '(' component_list ')'
functor ::- {token beginning with 'a' .. 'z'}
component_list ::- term | term ',' component_list
term ::- goal | list
list ::- '[]' | '[' element_list ']'
element_list ::- term | term ',' element_list | term | term
e.g.
SENTENCE
-> RULE
-> HEAD :- TAIL
-> GOAL :- GOAL
-> STRUCTURE :- STRUCTURE
-> FUNCTOR(COMPONENT_LIST) :- FUNCTOR(COMPONENT_LIST)
-> FUNCTOR(TERM,COMP_LIST) :- FUNCTOR(TERM,COMP_LIST)
-> FUNCTOR(TERM,TERM) :- FUNCTOR(TERM,TERM)
-> FUNCTOR(GOAL,GOAL) :- FUNCTOR(GOAL,GOAL)
-> FUNCTOR(CONST,VAR) :- FUNCTOR(VAR,CONST)
-> likes(john,X) :- likes(X,wine)

"JOHN LIKES PEOPLE WHO LIKE WINE".

OK here's an arithmetic grammar I'm working on!

EXPRESSION ::> SUM | TERM
SUM ::> TERM + TERM
TERM::> FACTOR FACTOR
FACTOR ::> TERM | (NUM)
NUM ::> -ABS | ABS
ABS ::> LEADINGDIGIT DIGIT^n | LEADINGDIGIT DIGIT^n . DIGITS | 0 .
DIGITS
LEADINGDIGIT ::> 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
DIGITS ::> DIGIT | DIGIT DIGITS
DIGIT ::> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
EXPRESSION
-> TERM
-> FACTOR FACTOR
-> (NUM) (NUM)
-> (-ABS) (-ABS)
-> (-LEADINGDIGIT DIGITS) (-LEADINGDIGIT DIGITS)
-> (-10) (-20)

OK so the Natural Numbers are from 10 onwards

********

ZFC would be just as easy with about 20 symbols!

All possible predicate calculus theorems and a bnf grammar for ZFC -
COUNTED!

OK so... where is 1 missing set you can't formulate?

Herc

Graham Cooper

unread,

May 20, 2012, 1:42:37 AM5/20/12

to

On May 20, 2:32 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:

> Note this encompasses Predicate Calculus.
>
> Courtesy: VTPROLOG, AI EXPERT MAGAZINE
> sentence ::- rule | query | command
> rule ::- head '.' | head ':-' tail '.'
> query ::- '?-' tail '.'
> command ::- '@' file_name '.'
> head ::- goal
> tail ::- goal | goal ',' tail
> goal ::- constant | variable | structure
> constant ::- {quoted string} | {token beginning with 'a' .. 'z'}
> variable ::- {identifier beginning with 'A' .. 'Z' or '_' }
> structure ::- functor '(' component_list ')'
> functor ::- {token beginning with 'a' .. 'z'}
> component_list ::- term | term ',' component_list
> term ::- goal | list
> list ::- '[]' | '[' element_list ']'
> element_list ::- term | term ',' element_list | term | term

If you're wondering where the logic symbols are.

i.e A FORMULA IN PREDICATE_LOGIC IS A -> B, A and B, A or B, ... etc.

AND is with a comma between clauses

tail ::- goal | goal ',' tail

OR is via duplicate predicate definitions.
eg.
wet(person) :- swimming(person)
wet(person) :- washing(person)

and NOT is not part of the language for some reason, only TRUE records
are returned, whole sets of answers are returned in Relational
Languages, like a SELECT QUERY in SQL!

PROLOG was made for PROGRAMMING LOGIC, similar to what MetaMath does
by pattern matching theorems.

PROLOG = LISP + UNIFY

e.g.

>TheTruth. **ENTER A FACT
>?- TheTruth. **QUERY A FACT

YES

It only knows YES and NO so far, but it talks!

Herc

WM

unread,

May 20, 2012, 2:36:58 AM5/20/12

to

> posing under your name?-

Du solltest Dich auf die deutsche Sprache beschränken, wenn du
englische Texte nicht verstehst.

Ich schrieb, dass Deine Beschuldigung, ich hätte andere als Idioten
bezeichnet, falsch sei. Du hast sie bisher nicht belegt. Ferner
schrieb ich, dass in Mathematics.StackExchange eine Bande von
kriminellen Subjekten meinen Namen unautorisiert missbraucht hat.
Alles, was auf meiner Homepage von mir unterzeichnet ist, wurde auch
von mir geschrieben.

Gruß, WM

karl

unread,

May 20, 2012, 3:43:13 AM5/20/12

to

Very funny, you complain that I accuse you wrongly of insulting people and you start insulting me. LOL.

For example:

>But instead of offering an
> apology, you continue with your insults and prefer to be an inveterate
> liar.

>Typical behaviour of members of the intellectual lower stratum.

>Du solltest Dich auf die deutsche Sprache beschränken, wenn du
> englische Texte nicht verstehst.

You have just shown your true face.

Ciao
Karl

WM

unread,

May 20, 2012, 6:42:23 AM5/20/12

to

On 20 Mai, 00:07, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

> Fine -- just spell that out in set theory --
> several of these are uncontroversial. Of course,
> you would need to be a bit more exact --
> " If each one is covered by an interval I_n of measure 10^-n, then there
> are at most countably many intervals I_n "
> for example has different readings,

unread,

May 20, 2012, 6:47:03 AM5/20/12

to

On 20 Mai, 06:32, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On May 20, 8:27 am, Jürgen R. <jurg...@arcor.de> wrote:
>
> > > The "proof" ends with p. 516. And
> > > obviously Zermelo takes for granted that every element can be
> > > addressed, i.e., is defined.
>
> > No. "Addressing", whatever that might mean, has nothing to do
> > with the argument. Nor is "addressing" of "elements" a notion
> > that has a meaning outside of M ckenhausen.
>
> There are Specification Languages but you end up programming the
> function in a 4GL like Prolog anyway.
>
> Here is a bnf grammar that could enumerate Prolog Horne Clauses.

It is useless to try to teach Rennenkampf mathematics.

Regards, WM

WM

unread,

May 20, 2012, 7:23:36 AM5/20/12

to

On 19 Mai, 22:33, Virgil <vir...@ligriv.com> wrote:
> " How can one define functions having domains and ranges which do not
> exist other than in WM's matheology?"
>
> And as asked unanswered!
> --

I told you: Read Euler, Gauss, Cauchy, Weierstrass to learn what a
function is and why completed infinity is not required.

Regards, WM

unread,

May 20, 2012, 10:04:48 AM5/20/12

to

On 20 Mai, 15:22, "dilettante" <n...@nonono.no> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message
>
> news:4a213eac-605e-4472...@p1g2000vbv.googlegroups.com...
> On 20 Mai, 00:27, "dilettante" <n...@nonono.no> wrote:
>
> > "WM" <mueck...@rz.fh-augsburg.de> wrote in message
>
> >news:47b0b804-0605-472d...@ec4g2000vbb.googlegroups.com...
>
> > >Every sentence that starts with the phrase "For all natural numbers"
> > >is false.
> > >Regards, WM
>
> > Surely there are countably many such sentences. Are you saying that ALL of
> > them are false?
> > And what about the sentences that begin with "Every sentence"? How many of
> > them are true?
>
> You should consult the author:
> A priori, every statement that starts "for every integer n" is
> completely meaningless.
> [Doron ZEILBERGER: "REAL" ANALYSIS Is A DEGENERATE CASE of DISCRETE
> ANALYSIS, ]http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf
>
> Regards, WM
> And statements that start "every statement that..."? Are those completely
> meaningless , a priori?

In Germany we have a proverb saying: "There is no proverb that has no
exception. Or remember Socrates who said "I know that I know nothing".
"Every statement" is kind of that kind.

Regards, WM

dilettante

unread,

May 20, 2012, 10:29:43 AM5/20/12

to

Still can't quite tell if you realize that the paper you linked to and
quoted, even though it touches on some interesting mathematics, was intended
primarily as a joke. The sentence you quote, 'Apriori, every statement that
starts "for every integer n" is completely meaningless' is the punch line.

"WM" <muec...@rz.fh-augsburg.de> wrote in message

news:09122278-bf23-4864...@n33g2000vbi.googlegroups.com...

karl

unread,

May 20, 2012, 10:54:41 AM5/20/12

to

Am 20.05.2012 16:29, schrieb dilettante:
> Still can't quite tell if you realize that the paper you linked to and quoted, even though it touches on some
> interesting mathematics, was intended primarily as a joke. The sentence you quote, 'Apriori, every statement that starts
> "for every integer n" is completely meaningless' is the punch line.
>

You really believe that WM has a sense of humor?

WM

unread,

May 20, 2012, 12:19:30 PM5/20/12

to

On 20 Mai, 16:29, "dilettante" <n...@nonono.no> wrote:
> Still can't quite tell if you realize that the paper you linked to and
> quoted, even though it touches on some interesting mathematics, was intended
> primarily as a joke. The sentence you quote, 'Apriori, every statement that
> starts "for every integer n" is completely meaningless' is the punch line.

You allude to Wittgenstein's view of set theory? For if one person can
see it as a paradise of mathematicians, why should not another see it
as a joke? [Ludwig Wittgenstein, Matheoogy § 012]

No, Doron's sentence is serious and true. Of course there are not
*all* numbers. Ask anybody to tell you where these "all numbers" are.
Ask anybody to name a natural number that would require more than
10^100 bits. It's simply as impossible as to write numbers with more
than 10 different digits on your pocket calculator.

Here you can find a related statement:
http://www.math.rutgers.edu/~zeilberg/Opinion68.html

Regards, WM

dilettante

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May 20, 2012, 2:21:29 PM5/20/12

to

Doron's sentence may or may not be serious, but it is a punchline whether he
knew it or not. It declares itself to be meaningless.

"WM" <muec...@rz.fh-augsburg.de> wrote in message

news:b02a9210-1c47-499b...@e20g2000vbm.googlegroups.com...

On 20 Mai, 16:29, "dilettante" <n...@nonono.no> wrote:
>> Still can't quite tell if you realize that the paper you linked to and
>> quoted, even though it touches on some interesting mathematics, was
>> intended
>> primarily as a joke. The sentence you quote, 'Apriori, every statement
>> that
>> starts "for every integer n" is completely meaningless' is the punch
>> line.

>You allude to Wittgenstein's view of set theory? For if one person can
>see it as a paradise of mathematicians, why should not another see it
>as a joke? [Ludwig Wittgenstein, Matheoogy � 012]

>No, Doron's sentence is serious and true. Of course there are not
>*all* numbers. Ask anybody to tell you where these "all numbers" are.
>Ask anybody to name a natural number that would require more than
>10^100 bits. It's simply as impossible as to write numbers with more
>than 10 different digits on your pocket calculator.

What does it mean for a natural number to "require N bits"? Are there any
natural numbers that require more than 10000 bits? If so, what is the
smallest one?

Jesse F. Hughes

unread,

May 20, 2012, 2:41:16 PM5/20/12

to

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

> No, Doron's sentence is serious and true. Of course there are not
> *all* numbers. Ask anybody to tell you where these "all numbers" are.

Brilliant! Sheer brilliance!

--
"There is also an 'advanced' list [of Clay Prize Challenges] that only
the most elite see, that contains much more difficult problems
e.g. the Halting Problem. Turing admitted that he could not solve it,
saying that for him the problem has been unsolvable." -- Charlie-Boo

LudovicoVan

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May 20, 2012, 3:58:58 PM5/20/12

to

"WM" <muec...@rz.fh-augsburg.de> wrote in message

news:17d08534-a802-48f2...@s9g2000vbg.googlegroups.com...

> On 19 Mai, 05:20, "LudovicoVan" <ju...@diegidio.name> wrote:
>> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

>> news:c76bf82d-cc13-4605-8f26-
>>
>> > But Cantor's finished infinity and list of all reals implies theism.
>>
>> In that sense, even the set N is a finished (complete) infinity and
>> implies
>> some kind of theism.
>
> Of course. Since Darwin we should do better.
>
> "Platonism is the medieval metaphysics of mathematics; surely we can
> do better" [Solomon Feferman, KB 090614]
> http://www.hs-augsburg.de/~mueckenh/KB/KB%20001-200.pdf

IMHO, that these thingies are logically invalid is the only mathematical
objection to raise. The rest is really philosophy.

>> That mathematics needs a philosophy of mathematics is
>> not, per se, a disease, is it?
>
> A philosophy is good, a religion, for mathematics, is bad.

You know, I'd venture that philosophy is the only sane religion for the
white/western man...

-LV

Marshall

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May 20, 2012, 3:38:07 PM5/20/12

to

On Saturday, May 19, 2012 5:35:38 AM UTC-7, Jesse F. Hughes wrote:
> WM <muec...@rz.fh-augsburg.de> writes:
>
> > Mathematicians know:

> > Every sentence that starts with the phrase "For all natural numbers"
> > is false.
>

> Well, I'm just a poor housewife[1], so I reckon I've no clear idea why
> that follows. Sentences such as, "Every natural number is either odd or
> even" and "Every natural other than zero is a successor" seem perfectly
> clear and true to me, but I guess smart ol' mathematicians know better.

How about "For all natural numbers n, if n = 2 then n+n = 4."

How about "For all natural numbers n, true."

Well, I guess there is some progress afoot. WM had to turn it up to
11 before he could get a flamewar going. That's ten consecutive
successes.

> Footnotes:
> [1] Just to be clear, I am male and use the term in a humorous sense.

I see you are anticipating the presence of the ever-literal TP, ha ha.

Marshall

WM

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May 20, 2012, 3:26:23 PM5/20/12

to

On 20 Mai, 20:21, "dilettante" <n...@nonono.no> wrote:
> Doron's sentence may or may not be serious, but it is a punchline whether he
> knew it or not. It declares itself to be meaningless.
>

> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

>
> news:b02a9210-1c47-499b...@e20g2000vbm.googlegroups.com...
> On 20 Mai, 16:29, "dilettante" <n...@nonono.no> wrote:
>
> >> Still can't quite tell if you realize that the paper you linked to and
> >> quoted, even though it touches on some interesting mathematics, was
> >> intended
> >> primarily as a joke. The sentence you quote, 'Apriori, every statement
> >> that
> >> starts "for every integer n" is completely meaningless' is the punch
> >> line.
> >You allude to Wittgenstein's view of set theory? For if one person can
> >see it as a paradise of mathematicians, why should not another see it
> >as a joke? [Ludwig Wittgenstein, Matheoogy 012]
> >No, Doron's sentence is serious and true. Of course there are not
> >*all* numbers. Ask anybody to tell you where these "all numbers" are.
> >Ask anybody to name a natural number that would require more than
> >10^100 bits. It's simply as impossible as to write numbers with more
> >than 10 different digits on your pocket calculator.
>
> What does it mean for a natural number to "require N bits"?

A binary string that is not defined by a certain definition like
"take a one and then three zeros"
or
"take the first ten digits of the binary expansion of 1/3"
must be written with bits like
1000
or
0.010101010.

If there is no shorter definition is available, you need bits.
If more than 10^100 bits are required, then the number has a due
complexity. (Related information can be found under "Kolmogorov
complexity.)

> Are there any
> natural numbers that require more than 10000 bits? If so, what is the
> smallest one?

There are natural numbers that require more than 100 bits. A
comfortable way to find the smallest one, is to list all smaller ones.
But it is tedious. Perhaps there are better means to answer your
question.

A simple model is the pocket calculator. Check the smallest number
that cannot be displayed.

Regards, WM

Virgil

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May 20, 2012, 7:06:36 PM5/20/12

to

In article
<92d6469e-cfcf-4310...@m3g2000vbl.googlegroups.com>,

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

> On 19 Mai, 22:33, Virgil <vir...@ligriv.com> wrote:
> > " How can one define functions having domains and ranges which do not
> > exist other than in WM's matheology?"

WM snipped what the following referred to.
> >
> > And as asked unanswered!

So I snipped him,.
--

Virgil

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May 20, 2012, 7:16:39 PM5/20/12

to

In article
<e56c073b-ab73-48a2...@z19g2000vbe.googlegroups.com>,

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

> On 19 Mai, 23:55, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <b4640e45-7c99-4024-a7a8-08f968b96...@b26g2000vbt.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > Unfortunately you have forgotten to mention how countably many
> > > intervals can separate uncountably many irrationals.
> >
> > Since any one rationally end-pointed interval, of which there are just
> > countably many, separates uncountably many smaller irrationals from
> > uncountably many larger irrationals, what is the problem?
>
>
> There are aleph_0 borders of intervals (of course these are rational
> numbers and as such also carry their own intervals - but that is of no
> interest). aleph_0 borders divide the unit interval and make aleph_0
> intervals. aleph_0 of them containing no rational number.

Actually, every interval of positive length contains infinitely many
rationals.

> You believe
> that there are 2^aleph_0 irrationals in those intervals but never more
> than one in per interval.

Actually I believe that there are more that aleph_0 irrationals in any
real interval of positive length

>
> If you beieve that, why don't you believe that there are 2^aleph_0
> entries in Cantor's list?

Because I can ennumerate the entries on Cantor's list, which makes the
number of elements in Cantor's list = Aleph_0 < 2^Aleph_0.

As even someone as incompetent as WM should know by now!

> You are really inconsistent.

No so much so as one who thinks Aleph_0 >= 2^Aleph_0.
>
> Regards, WM
--

Virgil

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May 20, 2012, 7:22:17 PM5/20/12

to

In article
<3d33b638-8015-4d84...@dg7g2000vbb.googlegroups.com>,

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

> On 20 Mai, 00:07, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> > That work would be very worthwhile, if it can be done.
> > You tell us that the contradictions are glaring, obvious etc.
>
> Do you need ZFC to understand Cantor's diagonal proof? No?
> My is the same. By aleph_0 borders of aleph_0 intervals around aleph_0
> rational aleph_0 intervals are created. (I cannot tell you any of
> them, but they are there like every well-ordering of the reals.) Some
> of them don't contain a rational number.

WM goofs again: The only real intervals failing to contain a rational
are of length 0 with an irrational endpoint.

> Consider only these
> intervals. They can be enumerated.

So WMis again claiming to be able to ennumerate the irrationals.

>They contain uncountably many
> irrational numbers.

Namely none.

> None of them contains more than one irrational
> number. Too difficult to understand?

I do understand that none is less that one (At least as numbers, though,
of course, not as words).
>
> Regards, WM
--

dilettante

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May 20, 2012, 7:26:32 PM5/20/12

to

You didn't answer my my question: What does it mean for a natural number to
"require N bits"?

unread,

May 20, 2012, 7:43:05 PM5/20/12

to

In article
<90b6b290-2eea-4d57...@eh4g2000vbb.googlegroups.com>,

It may be useless for someone who "knows" so much about mathematics
that is actually not true of mathematics as WM does.
--

Virgil

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May 20, 2012, 8:09:19 PM5/20/12

to

In article
<b60d961e-a316-4c8c...@s5g2000vbc.googlegroups.com>,

Aproof that this can be done has been presented several times and has
yet to be faulted.
--

Virgil

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May 20, 2012, 8:11:39 PM5/20/12

to

In article
<a612ea9d-c575-4f32...@n33g2000vbi.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 19 Mai, 23:58, Virgil <vir...@ligriv.com> wrote:
> > In article

> > <5f25a726-bebd-4cd7-83c4-3547ad63b...@b26g2000vbt.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > > Zermelo did so. In German "Beweis, dass jede Menge wohlgeordnet werden
> > > > > kann" means "it can be done".
> >
> > > > To claim that something can be done, or even that one has done it, is
> > > > merely a claim until it has been seen to have been done.
> >
> > > > Consider, for example, Fermat's last "theorem".
> > > > Fermat claimed to have a proof for it, but did he really have one?
> > > > The proof that was finally found by Andrew Wiles would have been
> > > > impossible for Fermat to have found.
> >
> > > And the proof that Zermelo pretended to have found is impossible for
> > > everybody (if R was in fact uncountable) because nobody can well-order
> > > what he cannot distinguish.
> >
> > Claimed but not proven.
>
> Can you give one counter example, i.e. well-order elements that you
> cannot identify?

Lack of a counter example is not regarded as proof of a claim,
at least in proper mathematics.
--

Virgil

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May 20, 2012, 8:20:41 PM5/20/12

to

In article
<2f1c6804-2eea-4d12...@v24g2000vbx.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> On 20 Mai, 00:41, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > Alan Smaill <sma...@SPAMinf.ed.ac.uk> writes:
> > > Consider Cantor's reaction to Russell's letter showing the
> > > flaw in Cantor's version of set theory.
> >
> > Er, wasn't that Frege?
>
> It was. Cantor did not react directly. But we should not try to
> confuse Alan before he gets clear about the impossibility to separate
> uncountably many irrationals by few intervals.

Note that since the set of rationals is countable, the set of real
intervals with rational endpoints also countable, and between any two
reals there are at least two rationals.

Thus between any two reals there is a rationaly endpointed interval, one
of a countable set of such rationaly endpointed intervals, separating
those reals.
--

Virgil

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May 20, 2012, 8:24:49 PM5/20/12

to

In article
<f32db557-fe45-4279...@e20g2000vbm.googlegroups.com>,

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

> On 20 Mai, 00:07, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>

> > Fine -- just spell that out in set theory --
> > several of these are uncontroversial. Of course,
> > you would need to be a bit more exact --
> > " If each one is covered by an interval I_n of measure 10^-n, then there
> > are at most countably many intervals I_n "
> > for example has different readings,
>
> You are in error. Perhaps you try to consider unions of intervals and
> limits and the like. But I don't. There are countably many intervals
> and uncountably many irrationals that are separated by those
> intervals. No ZFC will help you to veil this obvious mathematical
> truth.

It is still the case that the set of all rationally endpointed intervals
is countable and between any two distinct reals there is such a
rationally endpointed interval ( actually there are countably many).

So whatever separation property WM was trying to deny is trivially true
despite his attempted denial.
--

Graham Cooper

unread,

May 21, 2012, 12:22:33 AM5/21/12

to

On May 21, 9:16 am, Virgil <vir...@ligriv.com> wrote:
>
> Actually I believe that there are more that aleph_0 irrationals in any
> real interval of positive length

So you finally answered my Question from last week!

"There are more Reals than Naturals."

[VIRGIL]
If that means that there is a surjection from the reals to the
naturals
but no surjection from the naturals to the reals ,Yes!

What about this one?

"The set of Real Numbers is bigger than the set of Natural Numbers."
True or False?

Here is Dan Christenson's take

http://www.dcproof.com/PowerSetThm.html
'If p is the powerset of s, then there exists no function mapping s
to
every element of p.

Thus, the powerset of any set s, finite or otherwise, is always
larger
than s.'

So EXIST(x) x>oo ?

Say your |R| = 2X2X2X2...

>
>
>
> > If you beieve that, why don't you believe that there are 2^aleph_0
> > entries in Cantor's list?
>
> Because I can ennumerate the entries on Cantor's list, which makes the
> number of elements in Cantor's list = Aleph_0 < 2^Aleph_0.
>
> As even someone as incompetent as WM should know by now!
>
> > You are really inconsistent.
>
> No so much so as one who thinks Aleph_0 >= 2^Aleph_0.
>

My COMPUTABLE UTM^2 can permute N lists of N

That's 1X2X3X4X5X6.... sequences all computed.

Every (computable) Permutation of N.

2X2X2X2... IS A TINY PALTRY INFINITY COMPARED TO UTM^2!!
1X2X3X4...

Herc

Graham Cooper

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May 21, 2012, 12:43:49 AM5/21/12

to

On May 21, 4:41 am, "Jesse F. Hughes" wrote>

>
> Brilliant! Sheer brilliance!
>
> --
> "There is also an 'advanced' list [of Clay Prize Challenges] that only
> the most elite see, that contains much more difficult problems
> e.g. the Halting Problem. Turing admitted that he could not solve it,
> saying that for him the problem has been unsolvable." -- Charlie-Boo

That sounds like Clay... sell the Halt() Function to the highest
bidder between Oracle and MS, subtract $1M and pocket the profits!

Herc
--
www.tinyurl.com/HaltFunction
www.tinyurl.com/GodelStatement

Virgil

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May 21, 2012, 1:14:55 AM5/21/12

to

In article
<735647bf-e764-4f4f...@n9g2000pbi.googlegroups.com>,

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

> On May 21, 9:16 am, Virgil <vir...@ligriv.com> wrote:
> >
> > Actually I believe that there are more that aleph_0 irrationals in any
> > real interval of positive length
>
>
> So you finally answered my Question from last week!
>
> "There are more Reals than Naturals."
>
> [VIRGIL]
> If that means that there is a surjection from the reals to the
> naturals
> but no surjection from the naturals to the reals ,Yes!
>
> What about this one?
>
> "The set of Real Numbers is bigger than the set of Natural Numbers."
> True or False?

If you compare set sizes by comparing possible surjections, or possible
injections, then true, otherwise I need to know how you compare set
sizes before answering.
--

Graham Cooper

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May 21, 2012, 1:18:26 AM5/21/12

to

On May 21, 3:14 pm, Virgil <vir...@ligriv.com> wrote:
> In article

> <735647bf-e764-4f4f-996b-17c2a7bf9...@n9g2000pbi.googlegroups.com>,

> Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On May 21, 9:16 am, Virgil <vir...@ligriv.com> wrote:
>
> > > Actually I believe that there are more that aleph_0 irrationals in any
> > > real interval of positive length
>
> > So you finally answered my Question from last week!
>
> > "There are more Reals than Naturals."
>
> > [VIRGIL]
> > If that means that there is a surjection from the reals to the
> > naturals
> > but no surjection from the naturals to the reals ,Yes!
>
> > What about this one?
>
> > "The set of Real Numbers is bigger than the set of Natural Numbers."
> > True or False?
>
> If you compare set sizes by comparing possible surjections, or possible
> injections, then true, otherwise I need to know how you compare set
> sizes before answering.
>

there's more in the bigger one!

[VIRGIL]Actually I believe that there are more that aleph_0

Herc

Virgil

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May 21, 2012, 2:54:41 AM5/21/12

to

In article
<e5081f91-43cc-4d61...@f9g2000pbd.googlegroups.com>,

Then how do you figure out which one is bigger if you can't tell any
other way which one "has more"?
--