In every unit interval of the real axis there are more rationals than naturals.

[WM]

How can the belief of equinumerosity be reconciled with mathematics?

Regards, WM

[Me]

On Thursday, February 7, 2019 at 10:33:43 AM UTC+1, WM wrote:

> How can the belief of equinumerosity be [justified]?

By defining the notion of "equinumerosity" and a subsequent proof that Q n [x, x+1] is equinumerous with IN for all x e IR.

See: https://en.wikipedia.org/wiki/Equinumerosity

[Jew Lover]

On Thursday, 7 February 2019 04:33:43 UTC-5, WM wrote:
> How can the belief of equinumerosity be reconciled with mathematics?

Short answer: It can't.

"Bijective cardinality" has nothing to do with cardinality or equinumerosity.

Kronecker: "I don't know what prevails in Cantor's ..., but there is no mathematics there".

>
> Regards, WM

[WM]

But why have five generations of mathematicians forgotten all mathematical principles? This accomplishment will hardly be topped ever.

Regards, WM

[WM]

Am Donnerstag, 7. Februar 2019 12:24:07 UTC+1 schrieb Me:
> On Thursday, February 7, 2019 at 10:33:43 AM UTC+1, WM wrote:
>
> > How can the belief of equinumerosity be [justified]?
>
> By defining the notion of "equinumerosity"

By defining 1 = 8 fools at most can be made to believe in that equality. But not even fools would believe that the equal size of finite initial segments could indicate anything about the sizes of infinite sets.

Regards, WM

[jvr]

On Thursday, February 7, 2019 at 10:33:43 AM UTC+1, WM wrote:

> How can the belief of equinumerosity be reconciled with mathematics?
>

That depends entirely upon *your* definition of 'belief', 'equinumerosity' and
'mathematics'.
You have not and will not give a coherent definition of any
of those three words, i.e. you are trolling again.

[Jew Lover]

I think this powerpoint was one of your best:

https://www.hs-augsburg.de/~mueckenh/HI/HI12.PPT

I particularly like these quotes by Wittgenstein:

You can’t talk about all numbers, because there's no such thing as all numbers.

Set theory is wrong.

There is no path to infinity, not even an endless one.

I believe, and I hope, that a future generation will laugh at this hocus pocus.

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

Set theory is wrong and yet set theory and FOL is supposedly based on Wittgenstein's Logic! Chuckle.


>
> Regards, WM

[Jew Lover]

On Thursday, 7 February 2019 06:24:07 UTC-5, Me wrote:
> On Thursday, February 7, 2019 at 10:33:43 AM UTC+1, WM wrote:
>
> > How can the belief of equinumerosity be [justified]?
>
> By defining the notion of "equinumerosity" and a subsequent proof that Q n [x, x+1] is equinumerous with IN for all x e IR.

Bijective cardinality says nothing about "equinumerosity". Moreover, a moron like you cannot define anything. You will refrain from even attempts to define concepts because that is better left to your superiors - me! Chuckle.

Cantor's claim to fame: Any line segment can be scaled to any other line segment. Hail bijective cardinality. Was one of Cantor's ancestor perhaps a cartographer?

[Jew Lover]

How about you try a good dictionary? These words are in there.

[WM]

My definitions are those used by all mathematicians. But equinumerosity as applied by topologists in general and by Borel and Lebesgue in particular leads to a countable set of intervals with irrational limits or endpoints where all rational points of the real line have been captivated within a measure of 1. Outside nothing can exist, whether as points x or sets {x} or limits of whatever. This is a hair-rising claim.

By the way your objection that "in the infinite" other rules have to be applied would invalidate all of Cantor's arguments, in particular his diagonal argument. Because with other rules, "in the infinite" uncountably many entries could be accommodated in a list. Nobody could check that "in the infinite".

Regards, WM

[WM]

Am Donnerstag, 7. Februar 2019 15:19:32 UTC+1 schrieb Jew Lover:


> Cantor's claim to fame: Any line segment can be scaled to any other line segment. Hail bijective cardinality. Was one of Cantor's ancestor perhaps a cartographer?

Not only lines. All points of the diameter of a quark can be bijected to all points of the space-time continuum of the whole universe and even more.

A theory of incredible relevance for physics.

Regards, WM

[j4n bur53]

Well something with a diameter is not a point anymore.
Do you mean a small disk?

[Python]

Crank Doktor Frankenheim wrote:
> All points of the diameter of a quark can be bijected to all points of the space-time continuum of the whole universe and even more.
>
> A theory of incredible relevance for physics.

So a quark is a little sphere according to you. You are not
very relevant as a physicist, Herr Mueckenheim.

[WM]

Am Donnerstag, 7. Februar 2019 18:25:05 UTC+1 schrieb j4n bur53:
> Well something with a diameter is not a point anymore.
> Do you mean a small disk?

The diameter of quark is less than that of a Quarkstollen but it is not zero. Temporarily we assume less than 10^18 m.

But the true value is irrelevant. As long as it is larger than 0, there are uncountably many points. By the way a hair-raising discontinuity. Like McDuck or the Binary Tree or the vanishing of the intersection of endsegments.

Regards, WM

[bassam king karzeddin]

True, even if in modern mathematics (with a silly fiction as infinity) they make:
Limit (1/n) = 0, as (n)--> 00, where this definition "implies strictly" that:

(1/n) > 0, when (n)--> 00, and FOR SURE
BKK

[Ross A. Finlayson]

On Thursday, February 7, 2019 at 1:33:43 AM UTC-8, WM wrote:
> How can the belief of equinumerosity be reconciled with mathematics?
>
> Regards, WM

Why not it is a constant between density and partitioning,
here "infinity".

"Rationals" more than "naturals" as "the ordered field"
or "closure of naturals to division", the closure of the
naturals by the operation of division as resultingly the
ordered field of rationals with roots, here this constant
between signal density and integer measure is this way in
the terms of the equivalence of the density here the
"rational" numbers with their density, and integers, with,
in the space, the density.

Then the rationals are either
the uniformly dense or projectively dense,
here above uniformly as a property about
the near roots, the density of the roots,
the projectively dense then is about zero
as for example annihilator, besides that
it is its own multiplicative identity.

uniformly -> about the integers
projectively -> about zero

[Zelos Malum]

They haven't you imbecile.

[WM]

Am Freitag, 8. Februar 2019 07:37:39 UTC+1 schrieb Zelos Malum:


> > But why have five generations of mathematicians forgotten all mathematical principles? This accomplishment will hardly be topped ever.

>

> They haven't

They have. In mathematics we have the direct comparison criterion: If a sequence like McDuck's wealth grows for every n, then the limit cannot be empty. That is mathematics.

Matheology however "proves" the bijection between |N und |Q by showing that for finite initial segments the pairing is possible: (1, q1), (2, q2), ..., (n, qn). It is simply an incredible mistake to conclude from this on the infinite sets.

Regards, WM

[WM]

Am Donnerstag, 7. Februar 2019 20:24:27 UTC+1 schrieb bassam king karzeddin:


> True, even if in modern mathematics (with a silly fiction as infinity) they make:
> Limit (1/n) = 0, as (n)--> 00, where this definition "implies strictly" that:
>
> (1/n) > 0, when (n)--> 00

Of course every term of the sequence is positive.

But 0 is the only real number such that the difference to 1/n becomes smaller and smaller.

For every eps > 0 there is a natural number m such that for n > m
|1/n - 0| < eps.

For every other real number r, this cannot be accomplished. Therefore 0 has special relevance for this sequence.

Regards, WM

[Me]

On Friday, February 8, 2019 at 11:30:36 AM UTC+1, WM wrote:

> Mückenmatics however tries to "prove" the bijection between IN and (Q
> by showing that for finite initial segments the pairing is possible [...]

Of course an idiotic approach. It

> is simply an incredible mistake to conclude from this on the infinite sets.

Indeed! Great insight!

[WM]

Am Freitag, 8. Februar 2019 11:56:52 UTC+1 schrieb Me:
> On Friday, February 8, 2019 at 11:30:36 AM UTC+1, WM wrote:
>
> > Mückenmatics however tries to "prove" the bijection between IN and (Q
> > by showing that for finite initial segments the pairing is possible [...]

That is Cantor's approach: 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ...

> > is simply an incredible mistake to conclude from this on the infinite sets.
>
> Indeed! Great insight!

Alas, other tools are not available.

Regards, WM

[jvr]

It must be so because you can't think of an alternative.
Is that a valid argument in muckmeatical logic? You certainly use it a lot.

[Jew Lover]

How to do mainstream maths:

1. Take an existing well founded theory
2. think you are too smart and "distill" it into axioms
3. disregard the background
4. If you need to prove something and your axioms are not enough, either: create a new axiom or assume -- it's always good to assume. Without background there is nothing to keep you honest anyways.
5. Discover paradoxes. Oh look how smart you are. It's not nonsense, -- it's a paradox, the very proof that you are too smart for anybody else to make sense of it.

Don't forget to belong to a group. Nothing spells TRUTH better than group think.

[WM]

Am Freitag, 8. Februar 2019 14:22:18 UTC+1 schrieb jvr:
> On Friday, February 8, 2019 at 1:58:00 PM UTC+1, WM wrote:
> > Am Freitag, 8. Februar 2019 11:56:52 UTC+1 schrieb Me:
> > > On Friday, February 8, 2019 at 11:30:36 AM UTC+1, WM wrote:
> > >
> > > > Mückenmatics however tries to "prove" the bijection between IN and (Q
> > > > by showing that for finite initial segments the pairing is possible [...]
> >
> > That is Cantor's approach: 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ...
> >
> > > > is simply an incredible mistake to conclude from this on the infinite sets.
> > >
> > > Indeed! Great insight!
> >
> > Alas, other tools are not available.
>

> It must be so because

there is nothing else, no alephs and no omegas.

> you can't think of an alternative.
> Is that a valid argument in muckmeatical logic?

Cantor gas proved the infinite by means of the finite - like Euler, Cauchy, Weierstraß. No-one would have given a dime for a new theory of infinite delusions based on infinite illusions!

When happended the big rip?

Today the Jungvolk has grasped the facts. Cantor's results are self-contradictory unless they believe in the abrcadabra of simultaneity and action at a distance. Since the infinite delusions have established themselves as the basis of matheology they need no longer be supported by finitely provable arguments.

Regards, WM

[FredJeffries]

Even more, he claims to know whether the number of elementary particles in the universe is even or odd, although he refuses to divulge the answer...

[Jew Lover]

On Friday, 8 February 2019 12:57:04 UTC-5, WM wrote:
> Am Freitag, 8. Februar 2019 14:22:18 UTC+1 schrieb jvr:
> > On Friday, February 8, 2019 at 1:58:00 PM UTC+1, WM wrote:
> > > Am Freitag, 8. Februar 2019 11:56:52 UTC+1 schrieb Me:
> > > > On Friday, February 8, 2019 at 11:30:36 AM UTC+1, WM wrote:
> > > >
> > > > > Mückenmatics however tries to "prove" the bijection between IN and (Q
> > > > > by showing that for finite initial segments the pairing is possible [...]
> > >
> > > That is Cantor's approach: 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ...
> > >
> > > > > is simply an incredible mistake to conclude from this on the infinite sets.
> > > >
> > > > Indeed! Great insight!
> > >
> > > Alas, other tools are not available.
> >
> > It must be so because
>
> there is nothing else, no alephs and no omegas.
>
> > you can't think of an alternative.
> > Is that a valid argument in muckmeatical logic?
>
> Cantor gas proved the infinite by means of the finite - like Euler, Cauchy, Weierstraß. No-one would have given a dime for a new theory of infinite delusions based on infinite illusions!

The same thing happened with the espilon-delta proofs that supposedly rigorised calculus.

1. The standard "definition" f'(x)=lim_{h->0} [f(x+h)-f(x)]/h needs to know the limit (the derivative itself!!) and is circular.
2. The verification method is ALL about infinity and infinitesimals. You give me an epsilon and I'll find you a delta on this condition: delta and epsilon are both greater than 0. This is an infinite process. It doesn't stop at 0 because your finite difference quotient is undefined at 0.
3. You can make delta as small as you wish. Hmm, "infinitely small" ? Just bigger than 0?

[j4n bur53]

because it is a definiverification, says
somebody who even doesn't know what 3=<4 means.

[Jew Lover]

On Friday, 8 February 2019 13:32:59 UTC-5, jan burse driveled:
> because it is a definiverification, says...

In other words nonsense which we have grown accustomed to from you.

[a.n. other]

You can't even get that right!!! -1 is another number, such that the difference to 1/n becomes smaller and smaller as n->oo. Sheesh!

[j4n bur53]

Well a formula A(x) where you can proof:

A(x1) & A(x2) => x1 = x2

Is called an **implicit definition**. There
is nothing circular in it.

See also discussion on mi...@sci.logic, ever
heard about Alessandro Padoa?

https://ztfnews.wordpress.com/2013/10/14/alessandro-padoa-1868-1937/

You can of course also change the Weierstrass
definition into a more **explicit definition**,

For example this here:

lim n->oo sn = 1/3 where sn = sum_i=1^n 3/10^i

Is the same as

L.U.B. {sn} = 1/3

L.U.B. is explicit. Its just this set theoretic value:

L.U.B. {sn} = minimum intersect union [sn,oo)

https://en.wikipedia.org/wiki/Least-upper-bound_property

https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#The_case_of_sequences_of_real_numbers

[j4n bur53]

‘Padoa’s Method’, 3rd International Congress of
Philosophy, Paris 1900. ‘Logical introduction to
any deductive theory’.

He wrote also:

A. Padoa (1900) "Un Nouveau Système de Définitions
pour la Géométrie Euclidienne", Proceedings of the
International Congress of Mathematicians, tome 2, pages 353–63.

[Jew Lover]

Go back to sleep stupid birdbrain!

[j4n bur53]

Here is a little biography of Padoa:

http://hubertkennedy.angelfire.com/Eight_Mathematical.pdf

[j4n bur53]

Padoa method is underlying Evert Willem Beth
definability theorem:

"In mathematical logic, Beth definability is a
result that connects implicit definability of
a property to its explicit definability, specifically
the theorem states that the two senses of
definability are equivalent."
https://en.wikipedia.org/wiki/Beth_definability

[jvr]

On Friday, February 8, 2019 at 6:57:04 PM UTC+1, WM wrote:
> Am Freitag, 8. Februar 2019 14:22:18 UTC+1 schrieb jvr:
> > On Friday, February 8, 2019 at 1:58:00 PM UTC+1, WM wrote:
> > > Am Freitag, 8. Februar 2019 11:56:52 UTC+1 schrieb Me:
> > > > On Friday, February 8, 2019 at 11:30:36 AM UTC+1, WM wrote:
> > > >
> > > > > Mückenmatics however tries to "prove" the bijection between IN and (Q
> > > > > by showing that for finite initial segments the pairing is possible [...]
> > >
> > > That is Cantor's approach: 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, ...
> > >
> > > > > is simply an incredible mistake to conclude from this on the infinite sets.
> > > >
> > > > Indeed! Great insight!
> > >
> > > Alas, other tools are not available.
> >
> > It must be so because
>
> there is nothing else, no alephs and no omegas.
>
> > you can't think of an alternative.
> > Is that a valid argument in muckmeatical logic?
>
> Cantor gas proved the infinite by means of the finite - like Euler, Cauchy, Weierstraß. No-one would have given a dime for a new theory of infinite delusions based on infinite illusions!
>
> When happended the big rip?
>
> Today the Jungvolk has grasped the facts.

In case somebody doesn't know what this means: "Jungvolk" is a term
that every German immediately recognizes as Nazi lingo. The "Jungvolk"
was the 10-14yr age group in the Hitlerjugend.
No respectable person would ever use such a word today; Neo-Nazis use it
as a signal to the like-minded.

If you are interested in the use of language by the Fascists, read
Victor Klemperer: Lingua Tertii Imperii.

> Cantor's results are self-contradictory unless they believe in the
>abrcadabra of simultaneity and action at a distance.

That there are still quacks around who deny the possibility of
"action at a distance" is really unexpected. I know Mücke is ignorant and
not entirely sane. Or is it his rudimentary English that is failing him
once again?

[Jew Lover]

On Saturday, 9 February 2019 09:00:33 UTC-5, jvr wrote:
> >
> > Today the Jungvolk has grasped the facts.
>
> In case somebody doesn't know what this means: "Jungvolk" is a term
> that every German immediately recognizes as Nazi lingo.

Nonsense. It literally means "Young people". There is no association with Hitler Jungen.

[bassam king karzeddin]

On Friday, February 8, 2019 at 1:46:43 PM UTC+3, WM wrote:
> Am Donnerstag, 7. Februar 2019 20:24:27 UTC+1 schrieb bassam king karzeddin:
>
>
> > True, even if in modern mathematics (with a silly fiction as infinity) they make:
> > Limit (1/n) = 0, as (n)--> 00, where this definition "implies strictly" that:
> >
> > (1/n) > 0, when (n)--> 00
>
> Of course every term of the sequence is positive.
>
> But 0 is the only real number such that the difference to 1/n becomes smaller and smaller.

But the whole problem is mainly thinking that "zero" is any real meaningful number, where the fact it isn't any real number to be established, except by the wrong old conclusions (without any existing historical rigorous proof)

So to say, adopting an alleged "non-existing real number as zero" by assumption or conventions had given the mathematicians the chance to generate such obvious fictions as infinity, and later many infinities upon their desires to illegally well-establish many imperfect results and many illegal theorems in mathematics, where then they opened the doors widely to go endlessly in this wrong illegal direction to ill-establish many baseless huge volumes of so unnecessary mathematics that needs few centuries to come over from those silly MIND delusions of both (zeros and infinities), FOR SURE

>
> For every eps > 0 there is a natural number m such that for n > m
> |1/n - 0| < eps.
>
> For every other real number r, this cannot be accomplished. Therefore 0 has special relevance for this sequence.
>
> Regards, WM

The basic natural mathematics started by counting one (and never by the artificial human made number zero or negatives), where that one only can make the real numbers to a possible chosen scale (either by enlargening the one or minimizing it), and strictly only on a constructible EXISTING forms, (theoretically - and regardless of physical tools that has always an error of measurements), where this one can be enlarged to the natural numbers, where the DNA of its discrete natural numbers PROPERTIES would remain stored forever in any segment chosen line (which is a basically distance in the real physical existing sense), and no matter, however (short or long) is that distance expressed EXACTLY in terms of numbers, since neither both (shortest or longest) distances can be expressed in numbers, nor those both -say positive, (smallest or largest) real numbers exist either, SURE

So to say, it is quite many wrong questions in current wrong mathematics to ask whether there are more real numbers than prime numbers for examples since both are impossible existing sets to be comparable besides both were proven with "ENDLESS TERMS" undetermined numbers, FOR SURE

Regards
BKK

[WM]

Am Samstag, 9. Februar 2019 15:00:33 UTC+1 schrieb jvr:


> > Today the Jungvolk has grasped the facts.
>
> In case somebody doesn't know what this means: "Jungvolk" is a term
> that every German immediately recognizes as Nazi lingo. The "Jungvolk"
> was the 10-14yr age group in the Hitlerjugend.

The fanatism of the matheologians here around resembles that of the Jungvolk members.

> No respectable person would ever use such a word today;

Chuckle. The fanatism of the language warders in our days is of similar quality, by the way. It is a pleasure to provoke them. But it is not yet made punishable to deny actual infinity, is it?

Regards, WM

[blah]

On Friday, 8 February 2019 14:05:44 UTC-4, FredJeffries wrote:
> Even more, he claims to know whether the number of elementary particles in the universe is even or odd, although he refuses to divulge the answer...

Hell, if we posit the big bang, then the number of particles in the universe must be finite. It may change from one moment to the next, but it is still either even or odd at any moment. No need to divulge anything.

[WM]

Am Samstag, 9. Februar 2019 16:31:34 UTC+1 schrieb bassam king karzeddin:


> The basic natural mathematics started by counting one (and never by the artificial human made number zero or negatives),

That is true. Matheologians have started with zero in order to veil the inconsistenties of their pet theory, see "Why zero has been included in the set of natural numbers" in https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf , p. 240.

But when you have nothing and you get one Euro and afterwards you spend one Euro then you have obviously no Euro. Another word for that is zero Euro(s).

Regards, WM

[Jew Lover]

On Saturday, 9 February 2019 12:09:20 UTC-5, WM wrote:
> Am Samstag, 9. Februar 2019 15:00:33 UTC+1 schrieb jvr:
>
>
> > > Today the Jungvolk has grasped the facts.
> >
> > In case somebody doesn't know what this means: "Jungvolk" is a term
> > that every German immediately recognizes as Nazi lingo. The "Jungvolk"
> > was the 10-14yr age group in the Hitlerjugend.
>
> The fanatism of the matheologians here around resembles that of the Jungvolk members.

How would you say "young people" differently in German?

[WM]

Am Samstag, 9. Februar 2019 18:56:46 UTC+1 schrieb Jew Lover:
> On Saturday, 9 February 2019 12:09:20 UTC-5, WM wrote:
> > Am Samstag, 9. Februar 2019 15:00:33 UTC+1 schrieb jvr:
> >
> >
> > > > Today the Jungvolk has grasped the facts.
> > >
> > > In case somebody doesn't know what this means: "Jungvolk" is a term
> > > that every German immediately recognizes as Nazi lingo. The "Jungvolk"
> > > was the 10-14yr age group in the Hitlerjugend.
> >
> > The fanatism of the matheologians here around resembles that of the Jungvolk members.
>
> How would you say "young people" differently in German?
>

Junge Leute. Also "das junge Völkchen" is allowed by the guardians of public morals. Goethe: "Denn wie ich bei der Linde das junge Völkchen finde".

Even "das junge Volk" is allowed: https://www.augsburger-allgemeine.de › Lokales (Aichach) 04.09.2011 - Volksmusik geht das junge Volk aus.

Regards, WM

[jvr]

You are not going to be punished for using Nazi terminology nor for your
bigoted pseudo-mathematical diatribes; you are going to be despised,
however.
every

[Jew Lover]

False. I am certain all WM's students love him. I do too (even though I was never his student) and there are topics where I have different opinions to WM.

On the other hand, I despise Nazis like you!

> every

[WM]

Am Samstag, 9. Februar 2019 21:12:55 UTC+1 schrieb jvr:


> You are not going to be punished for using Nazi terminology nor for your
> bigoted pseudo-mathematical diatribes;

Who knows?

"No punishment, within legal boundaries {{death penalty, if in suitable states of the USA?}}, would be too severe for you for your wrongdoings. [...] Rest assured that my contact, the senior German civil servant who refused to believe this fiasco was going on, is being copied into these threads. I sincerely hope there are severe repercussions. Those exposed to this type of 'education', assuming they are, or their guardians if they are minors, have every right to seek legal remedies in the civil courts against the perpetrator(s)." [Port563 in "What is a real number", sci.math (9 May 2014)]

> you are going to be despised, however.

By whom?

"There are points in the complement C that are neither endpoints of intervals nor interior points of C." [Jürgen Rennenkampff in "Clusters and Cantor dust", sci.logic (5 Jan 2019)]

Regards, WM

[jvr]

On Sunday, February 10, 2019 at 9:43:34 AM UTC+1, WM wrote:
> Am Samstag, 9. Februar 2019 21:12:55 UTC+1 schrieb jvr:
>
>
> > You are not going to be punished for using Nazi terminology nor for your
> > bigoted pseudo-mathematical diatribes;
>
> Who knows?

I know.

But I can also understand that you cannot accurately express your
attitudes and opinions without recourse to Nazi terminology. If you
feel unjustly constrained by the "word police", by politically correct
do-gooders, who see a dangerous fascist in every provincial windbag -
be a man, stand your ground, sing "Die Fahne hoch" in public. Let people know who you are. Make Germany great again! Maybe you can be the German
Donald Trump!

>
> "No punishment, within legal boundaries {{death penalty, if in suitable states of the USA?}}, would be too severe for you for your wrongdoings. [...] Rest assured that my contact, the senior German civil servant who refused to believe this fiasco was going on, is being copied into these threads. I sincerely hope there are severe repercussions. Those exposed to this type of 'education', assuming they are, or their guardians if they are minors, have every right to seek legal remedies in the civil courts against the perpetrator(s)." [Port563 in "What is a real number", sci.math (9 May 2014)]

No, Mücke, you are not Giordano Bruno. You are a Usenet Quack, a Troll
without influence and with no audience. That is your punishment!

>
> > you are going to be despised, however.
>
> By whom?

By me and by every other reasonably sane person.

>
> "There are points in the complement C that are neither endpoints of intervals nor interior points of C." [Jürgen Rennenkampff in "Clusters and Cantor dust", sci.logic (5 Jan 2019)]

Yes, indeed; and in the explicit example of the Cantor Ternary set these
points are the non-terminating ternary fractions without 1's.

But don't worry about it, Mücke, this isn't in the remedial math syllabus.

[WM]

Am Sonntag, 10. Februar 2019 14:55:12 UTC+1 schrieb jvr:


> > "There are points in the complement C that are neither endpoints of intervals nor interior points of C." [Jürgen Rennenkampff in "Clusters and Cantor dust", sci.logic (5 Jan 2019)]
>
> Yes, indeed; and in the explicit example of the Cantor Ternary set these
> points are the non-terminating ternary fractions without 1's.

Non-terminating fractions without finite definitions cannot define real numbers. Simply try to find an example.

If you can I will accept your points of C that are neither inside nor endpoints. But first show it.

Regards, WM

[jvr]

Who cares what you "accept"?

We know that you can't understand the properties of the ternary set and,
more generally, the properties of nowhere dense perfect sets.

All such sets are uncountable and this has nothing to do with real
numbers, and certainly nothing with names of either reals or any
other red herrings.

Incidentally, the uncountability proof doesn't relies neither upon
the diagonal argument nor on any numerical representation of the reals.
But, of course, that belongs to the 99.9% of topology that you know
nothing about.

[WM]

Am Sonntag, 10. Februar 2019 17:03:43 UTC+1 schrieb jvr:
> On Sunday, February 10, 2019 at 4:27:47 PM UTC+1, WM wrote:
> > Am Sonntag, 10. Februar 2019 14:55:12 UTC+1 schrieb jvr:
> >
> >
> > > > "There are points in the complement C that are neither endpoints of intervals nor interior points of C." [Jürgen Rennenkampff in "Clusters and Cantor dust", sci.logic (5 Jan 2019)]
> > >
> > > Yes, indeed; and in the explicit example of the Cantor Ternary set these
> > > points are the non-terminating ternary fractions without 1's.
> >
> > Non-terminating fractions without finite definitions cannot define real numbers. Simply try to find an example.
> >
> > If you can I will accept your points of C that are neither inside nor endpoints. But first show it.
>
> Who cares what you "accept"?

Everybody who understands his own arguments and who is able to explain them to a non-technical audience. Obviously you can neither explain your claim nor give an example of an infinite digit sequence without finite definition that defines a real number.

Regards, WM

[j4n bur53]

We can give a finite definition that defines a real number,
where you don't know the infinite digit sequence.

So your claim is wrong that finite definitions would
knowledgeably define infinite digit sequences.

Lets say you have this finite expression, for a value
n where n is a natural number from {1,2,3,4,...} do
the following, compute the sequence n0=n, n1, n2, ...
where we have:

/ nk/2 for nk even
nk+1 = <
\ 3*nk+1

Now define a binary number as follows:

0.d1 d2 ....

Where dj = 1 if the sequence n0=j, n1, n2, ..., nk=1
reaches 1 one time. And dj = 0 if the sequence
n0=j, n1, n2, ... doesn't reach 1 one time.

Whats the real number of the above decimal representation?

[j4n bur53]

If you would say the real number is 1/9,
then you would have proved the Collatz conjecture.

Wikipedia Collatz conjecture
https://en.wikipedia.org/wiki/Collatz_conjecture

Tao The Collatz conjecture, ...
https://terrytao.wordpress.com/2011/08/25/the-collatz-conjecture-littlewood-offord-theory-and-powers-of-2-and-3/

[FredJeffries]

On Saturday, February 9, 2019 at 7:31:34 AM UTC-8, bassam king karzeddin wrote:

> But the whole problem is mainly thinking that "zero" is any real meaningful number, where the fact it isn't any real number to be established, except by the wrong old conclusions (without any existing historical rigorous proof)
>
> So to say, adopting an alleged "non-existing real number as zero" by assumption or conventions had given the mathematicians the chance to generate such obvious fictions as infinity, and later many infinities upon their desires to illegally well-establish many imperfect results and many illegal theorems in mathematics, where then they opened the doors widely to go endlessly in this wrong illegal direction to ill-establish many baseless huge volumes of so unnecessary mathematics that needs few centuries to come over from those silly MIND delusions of both (zeros and infinities), FOR SURE

Still waiting for you to show us how to do long multiplication or long division with your 'new' representation.

[Zelos Malum]

>They have.

They haven't, just because you want it to be finite and computer based does not mean that mathematics has abandoned things.

>Matheology however "proves" the bijection between |N und |Q by showing that for finite initial segments the pairing is possible: (1, q1), (2, q2), ..., (n, qn). It is simply an incredible mistake to conclude from this on the infinite sets.

They prove it by showing there is a surjection from |N to Q and one from Q to |N, then the sits are of the same cardinality and there exists a bijection between them.

[Zelos Malum]

Den fredag 8 februari 2019 kl. 15:32:33 UTC+1 skrev Jew Lover:
> On Friday, 8 February 2019 05:30:36 UTC-5, WM wrote:
> > Am Freitag, 8. Februar 2019 07:37:39 UTC+1 schrieb Zelos Malum:
> >
> >
> > > > But why have five generations of mathematicians forgotten all mathematical principles? This accomplishment will hardly be topped ever.
> >
> > >
> > > They haven't
> >
> > They have. In mathematics we have the direct comparison criterion: If a sequence like McDuck's wealth grows for every n, then the limit cannot be empty. That is mathematics.

> >
> > Matheology however "proves" the bijection between |N und |Q by showing that for finite initial segments the pairing is possible: (1, q1), (2, q2), ..., (n, qn). It is simply an incredible mistake to conclude from this on the infinite sets.
> >

> > Regards, WM
>
> How to do mainstream maths:
>
> 1. Take an existing well founded theory
> 2. think you are too smart and "distill" it into axioms
> 3. disregard the background
> 4. If you need to prove something and your axioms are not enough, either: create a new axiom or assume -- it's always good to assume. Without background there is nothing to keep you honest anyways.
> 5. Discover paradoxes. Oh look how smart you are. It's not nonsense, -- it's a paradox, the very proof that you are too smart for anybody else to make sense of it.
>
> Don't forget to belong to a group. Nothing spells TRUTH better than group think.

Point out a single proper paradox in modern mathematics, just one that is not you misunderstanding thigns and you will win awards.

[Zelos Malum]

>1. The standard "definition" f'(x)=lim_{h->0} [f(x+h)-f(x)]/h needs to know the limit (the derivative itself!!) and is circular.

Wrong, it is not circular (does not rely on itself), and it doesn't say one need to know it, it just says that whatever fits that criteria IS the derivative.

>2. The verification method is ALL about infinity and infinitesimals. You give me an epsilon and I'll find you a delta on this condition: delta and epsilon are both greater than 0. This is an infinite process. It doesn't stop at 0 because your finite difference quotient is undefined at 0.

It does not rely on any infinitesimal (standard calculus was specifically made to avoid them)

>3. You can make delta as small as you wish. Hmm, "infinitely small" ? Just bigger than 0?

Nope, it is always a rael number.

[Jew Lover]

On Monday, 11 February 2019 01:45:03 UTC-5, Zelos Malum wrote:

> Point out a single proper paradox in modern mathematics, just one that is not you misunderstanding thigns and you will win awards.

Many flaws have been pointed out. You simply cup your ears and refuse to listen.

> >1. The standard "definition" f'(x)=lim_{h->0} [f(x+h)-f(x)]/h needs to know the limit (the derivative itself!!) and is circular.
>
> Wrong, it is not circular (does not rely on itself), and it doesn't say one need to know it, it just says that whatever fits that criteria IS the derivative.

Nonsense. Chapter 7 of my free eBook debunks all of the rot. I am not going to waste time discussing it. It is circular because one DOES have to know the limit.

>
> >2. The verification method is ALL about infinity and infinitesimals. You give me an epsilon and I'll find you a delta on this condition: delta and epsilon are both greater than 0. This is an infinite process. It doesn't stop at 0 because your finite difference quotient is undefined at 0.
>
> It does not rely on any infinitesimal (standard calculus was specifically made to avoid them)

I'm sorry, but it does.

https://www.youtube.com/watch?v=rx8zpC19Blc

>
> >3. You can make delta as small as you wish. Hmm, "infinitely small" ? Just bigger than 0?
>
> Nope, it is always a rael number.

Nope. It is always some magnitude, not a real number because real numbers do not exist.

[transf...@gmail.com]

Am Sonntag, 10. Februar 2019 18:16:35 UTC+1 schrieb j4n bur53:
> We can give a finite definition that defines a real number,
> where you don't know the infinite digit sequence.

That is not doubted and does not disprove the fact that no digit sequence without finite definition can determinea real number.

>
> So your claim is wrong that finite definitions would
> knowledgeably define infinite digit sequences.

I did not claim that. Are you really a friend of logic? I claim that infinite digit sequences without finite definitions cannot determine real numbers.

Only when refusing this simple fact and further refusing the even simpler fact that a member of the set C either is within C or is a limit of C, transfinite set theory can be accepted. That means transfinite set theory can only be accepted by very stupid or very fanatic people.

Regards, WM

[transf...@gmail.com]

Am Sonntag, 10. Februar 2019 19:16:00 UTC+1 schrieb FredJeffries:


>
> Still waiting for you to show us how to do long multiplication or long division with your 'new' representation.

Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.

Can the belief in such obvious contradictions be topped by anything?

Regards, WM

[transf...@gmail.com]

Am Montag, 11. Februar 2019 07:40:38 UTC+1 schrieb Zelos Malum:
> >They have.
>
> They haven't, just because you want it to be finite and computer based does not mean that mathematics has abandoned things.
>
> >Matheology however "proves" the bijection between |N und |Q by showing that for finite initial segments the pairing is possible: (1, q1), (2, q2), ..., (n, qn). It is simply an incredible mistake to conclude from this on the infinite sets.
>
> They prove it by showing there is a surjection from |N to Q and one from Q to |N,

How do they "show" this? Only for every finite initial Segment - because more is impossible. Here is a line from Cantor:

(r1, r2, ..., r, ...) = (1/2, 1/3, 1/4, 2/3, 1/5, 1/6, 2/5, 3/4, ...)

Anything infinite???

> then the sits are of the same cardinality and there exists a bijection between them.

And then come the Problems. The Binary Tree: Aleph_0 nodes, i.e., start ups of distinguishable paths. But uncountably many ends.

Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.

These things are so obvious, that every sober mind sees the causes. But you will stay in the crowd of stupids who refuse to understand?

Regards, WM

[bassam king karzeddin]

On Sunday, February 10, 2019 at 8:16:35 PM UTC+3, j4n bur53 wrote:
> We can give a finite definition that defines a real number,
> where you don't know the infinite digit sequence.
>
> So your claim is wrong that finite definitions would
> knowledgeably define infinite digit sequences.
>
> Lets say you have this finite expression, for a value
> n where n is a natural number from {1,2,3,4,...} do
> the following, compute the sequence n0=n, n1, n2, ...
> where we have:
>
> / nk/2 for nk even
> nk+1 = <
> \ 3*nk+1
>
> Now define a binary number as follows:
>
> 0.d1 d2 ....

Still arguing aimlessly, wonder!

Can't you work your nonsense (> 0.d1 d2 ....) without a decimal notation for a few seconds only to see clearly how much your brain fart is truly astray?

Look, many clever school students can work without a decimal notation now, and they indeed saw everything much clearer and all that big theorems to convince a stubborn fanatic also

Don't let the school students or laypersons teach you soon the ever simplest lessons

And don't let that too tiny dot (.) of decimal notation blook completely your mind FOR SURE

But take a free lesson here since everything is already exposed

0235 = 235/1000 = 47/200 (IN SIMPLE FORM)

So, dear (pi) = 3141 ... /1000... =? (Guess what?), here are four choices especially for you

1) banana
2) tomato
3) tree
4) j4n burs5*s
*******************************

Good luck

BKK

[Jew Lover]

On Monday, 11 February 2019 08:39:36 UTC-5, transf...@gmail.com wrote:
> Am Sonntag, 10. Februar 2019 18:16:35 UTC+1 schrieb j4n bur53:
> > We can give a finite definition that defines a real number,
> > where you don't know the infinite digit sequence.
>
> That is not doubted and does not disprove the fact that no digit sequence without finite definition can determinea real number.

It's untrue that a "real" number can be expressed using a formula. The formula merely tells one the same thing as does a sequence and no sequence is finite in the case of an incommensurable magnitude.

> >
> > So your claim is wrong that finite definitions would
> > knowledgeably define infinite digit sequences.
>
> I did not claim that. Are you really a friend of logic? I claim that infinite digit sequences without finite definitions cannot determine real numbers.

Neither can formulas. Any given formula can only approximate a given incommensurable magnitude. It matters nothing that a convergent sequence is produced by a formula, because the "limit" may not be a rational number.

[WM]

Am Montag, 11. Februar 2019 17:40:11 UTC+1 schrieb Jew Lover:
> On Monday, 11 February 2019 08:39:36 UTC-5, transf...@gmail.com wrote:
> > Am Sonntag, 10. Februar 2019 18:16:35 UTC+1 schrieb j4n bur53:
> > > We can give a finite definition that defines a real number,
> > > where you don't know the infinite digit sequence.
> >
> > That is not doubted and does not disprove the fact that no digit sequence without finite definition can determinea real number.
>
>
> It's untrue that a "real" number can be expressed using a formula. The formula merely tells one the same thing as does a sequence and no sequence is finite in the case of an incommensurable magnitude.
>
> > >
> > > So your claim is wrong that finite definitions would
> > > knowledgeably define infinite digit sequences.
> >
> > I did not claim that. Are you really a friend of logic? I claim that infinite digit sequences without finite definitions cannot determine real numbers.
>
> Neither can formulas.

Take the finite formula: "0.111 and so on in infinity". Every one can find every desired digit. But if there are arbitrarily many digits (there is never a last one) then you cannot find out how to continue.

Regards, WM

[Jew Lover]

Not so. The sequence 0.111... is a consequence of trying to measure a rational number in base 10, that is, 1/9.

But I don't see how this is relevant? I am saying that you cannot define an incommensurable number using a formula

>
> Regards, WM

[konyberg]

But it is equal to 1/9, isn't it?
KON

[Jew Lover]

No, it isn't. 0.111... taken to any number of n places does not equal 1/9. Since there is no such thing as infinity, the case of all the ones being there is hypothetical. And then there is the theorem which states that 1/9 cannot be measured using base 10 because none of the prime factors of 9 are prime factors of 10.

By Euler's decree:

S = 0.1111...
Lim S = 1/9

S = Lim S => 0.111...= 1/9

> KON

[Zelos Malum]

>Many flaws have been pointed out. You simply cup your ears and refuse to listen.

Incorrect, thigns you THINK is a flaw due to your lack of understanding has been pointed out, not genuine flaws.

>Nonsense. Chapter 7 of my free eBook debunks all of the rot. I am not going to waste time discussing it. It is circular because one DOES have to know the limit.

Not at all, circular means it uses itself in the definition which it does not. The definition does not CARE NOR NEED how we ACQUIRE the limit, it is only there to tell if it IS the limit or NOT.

>I'm sorry, but it does.

It does not, it only deals with real numbers.

>Nope. It is always some magnitude, not a real number because real numbers do not exist.

It is a real number and they are perfectly constructible.

[bassam king karzeddin]

You are still suffering a lot to understand things that are the scope of school students

Just try to make without that devilish decimal point "mind blocking notation"

Designed especially for the ALLEGED genius mathematicians as you, and see it again so carefully

Hint: (0.111... = 111.../1000... and guess what is this number, here 4 choices for you

1) Train
2) Tree
3) Troll
4) Zelos

Good luck, stubborn moron, FOR SURE
BKK

[Jew Lover]

Zelos Malum is the poster boy of mainstream academic cranks. A lost cause...

[FredJeffries]

On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:
> Am Sonntag, 10. Februar 2019 19:16:00 UTC+1 schrieb FredJeffries:
>
>
> >
> > Still waiting for you to show us how to do long multiplication or long division with your 'new' representation.
>
> Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.

Why should *I* attempt to "explain" such nonsensical gibberish?

When are *YOU* going to tell us whether the number of elementary particles in the universe is even or odd?

[WM]

Am Dienstag, 12. Februar 2019 17:19:12 UTC+1 schrieb FredJeffries:
> On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:

> > Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.
>
> Why should *I* attempt to "explain" such nonsensical gibberish?

It is the essence of transfinite set theory. Nice to see that you have stopped to defend that nonsense.

Regards, WM

[WM]

Of course. 1/9 is that real number that is approached closer and closer. But the sequence has afinite definition.

>
> But I don't see how this is relevant? I am saying that you cannot define an incommensurable number using a formula

I can, for instance by SUM (1/n!). But my claim is that without a finite formula no real number can be defined by a digit sequence.

Regards, WM

[WM]

Am Dienstag, 12. Februar 2019 07:34:15 UTC+1 schrieb Zelos Malum:
> >Many flaws have been pointed out. You simply cup your ears and refuse to listen.
>
> Incorrect, thigns you THINK is a flaw due to your lack of understanding has been pointed out, not genuine flaws.

You are blind, like your fellow matheologians.

It is impossible that ℵ0 atoms separate 2^ℵ0 atoms. No sophism with limits can change this fact. That is easily seen by the clumsy answers collected here: https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 329. They will not convince any intelligent person with full brain functions.

Regards, WM

[WM]

Am Montag, 11. Februar 2019 21:42:51 UTC+1 schrieb konyberg:
> mandag 11. februar 2019 19.10.47 UTC+1 skrev WM følgende:


> > Take the finite formula: "0.111 and so on in infinity". Every one can find every desired digit. But if there are arbitrarily many digits (there is never a last one) then you cannot find out how to continue.

>

> But it is equal to 1/9, isn't it?

It is not equal to 1/9 because every digit fails to accomplish this result. In logic, contrary to matheology, we conclude that a linear set of flops will not represent a success.

It is put equal to 1/9 by definition because the limit of this sequence is 1/9.

Regards, WM

[FredJeffries]

On Tuesday, February 12, 2019 at 8:51:13 AM UTC-8, WM wrote:
> Am Dienstag, 12. Februar 2019 17:19:12 UTC+1 schrieb FredJeffries:
> > On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:
>
> > > Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.
> >
> > Why should *I* attempt to "explain" such nonsensical gibberish?
>
> It is the essence of transfinite set theory.

No, it isn't. It is gibberish promulgated by only you.

> Nice to see that you have stopped to defend that nonsense.

I have never "defended" it.

Is the number of elementary particles in the universe even or odd?

[FredJeffries]

On Thursday, February 7, 2019 at 9:07:31 AM UTC-8, WM wrote:
> Am Donnerstag, 7. Februar 2019 14:32:54 UTC+1 schrieb jvr:
> > On Thursday, February 7, 2019 at 10:33:43 AM UTC+1, WM wrote:
> > > How can the belief of equinumerosity be reconciled with mathematics?
> > >
> > That depends entirely upon *your* definition of 'belief', 'equinumerosity' and
> > 'mathematics'.
> > You have not and will not give a coherent definition of any
> > of those three words,
>
> My definitions are those used by all mathematicians.

Uh huh. Like all the "mathematicians" who "use" YOUR mangled daffynitions of "Intercession" and "Imaginärteil" and "Continuous function"?

[WM]

Am Dienstag, 12. Februar 2019 18:05:42 UTC+1 schrieb FredJeffries:
> On Tuesday, February 12, 2019 at 8:51:13 AM UTC-8, WM wrote:
> > Am Dienstag, 12. Februar 2019 17:19:12 UTC+1 schrieb FredJeffries:
> > > On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:
> >
> > > > Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.
> > >
> > > Why should *I* attempt to "explain" such nonsensical gibberish?
> >
> > It is the essence of transfinite set theory.
>
> No, it isn't. It is gibberish promulgated by only you.

The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]

To have an example with a simpler ratio consider Scrooge McDuck who per day earns 10 $ and spends 1 $. The dollar bills are enumerated by the natural numbers. McDuck receives and spends them in natural order. If he lived forever he would go bankrupt. (Using coins he would get rich.)

Regards, WM

[Me]

On Tuesday, February 12, 2019 at 6:01:59 PM UTC+1, WM wrote:

> ℵ0 atoms separate 2^ℵ0 atoms

Oh, you are dealing with atomic physics?

[Me]

Or of the set IN of natural numbers, etc.

[WM]

Eeplacing the lengthy expression "cluster or separated (degenerate) interval or point of Cantor-dust" by "atom" we get the theorem:

(1) Removing ℵ0 atoms separates 2^ℵ0 atoms in the complement.
(2) Removing 2^ℵ0 atoms separates ℵ0 atoms in the complement.

(2) follows by symmetry, for instance when removing what in (1) has remained. Therefore we can state the general rule: Removing N atoms leaves N or 2N or log2N atoms, depending on N. If we stop however in (2) after having removed ℵ0 atoms, we have, according to (1), separated more atoms in the complement, namely 2^ℵ0, than after finishing.

Regards, WM

[Me]

On Tuesday, February 12, 2019 at 6:41:53 PM UTC+1, WM wrote:

> (2) follows by symmetry

Yeah, another concept from pyhsics.

[WM]

Could you accept mathematics without this basic concept?

Mathematics is the part of physics where experiments are cheap. [V.I. Arnold: "On teaching mathematics" (1997)]

Nevertheless mathematics is sometimes too difficult for mathematicians, as Hilbert remarked. So listen what physicicists can tell you:

The ordinary diagonal Verfahren I believe to involve a patent confusion of the program and object aspects of the decimal fraction, which must be apparent to any who imagines himself actually carrying out the operations demanded in the proof. In fact, I find it difficult to understand how such a situation should have been capable of persisting in mathematics. [P.W. Bridgman (Nobel laureate): "A physicist's second reaction to Mengenlehre", Scripta Mathematica 2 (1934) p. 225ff]

Pure mathematics and science are finally being reunited and, mercifully, the Bourbaki plague is dying out. [M. Gell-Mann (Nobel laureate): "Nature conformable to herself", Bulletin of the Santa Fe Institute 7 (1992) p. 7]

The pure mathematician can do what he pleases, but the applied mathematician must be at least partially sane. [J.W. Gibbs]

Try it! Instead of preaching more separate paths than occasions to separate.

Regards, WM

[FredJeffries]

On Tuesday, February 12, 2019 at 9:15:47 AM UTC-8, WM wrote:
> Am Dienstag, 12. Februar 2019 18:05:42 UTC+1 schrieb FredJeffries:
> > On Tuesday, February 12, 2019 at 8:51:13 AM UTC-8, WM wrote:
> > > Am Dienstag, 12. Februar 2019 17:19:12 UTC+1 schrieb FredJeffries:
> > > > On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:
> > >
> > > > > Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.
> > > >
> > > > Why should *I* attempt to "explain" such nonsensical gibberish?
> > >
> > > It is the essence of transfinite set theory.
> >
> > No, it isn't. It is gibberish promulgated by only you.
>
> The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]

Dishonest, irrelevant misquotations. Absolutely nothing there about "McDuck's bankrupt" or "Binary Tree with aleph_0 nodes" or "aleph_0 separators of irrational numbers"...

> To have an example with a simpler ratio consider Scrooge McDuck who per day earns 10 $ and spends 1 $. The dollar bills are enumerated by the natural numbers. McDuck receives and spends them in natural order. If he lived forever he would go bankrupt. (Using coins he would get rich.)

Your imaginary friend McDuck never GOES bankrupt

[Serg Io]

how is your "New Calculus" doing since it was exposed in the press as
"Fake Calculus"


[AP WIRE: for release 5-3-2018, "Fake Calculus" Exposed misleading black
teens]

https://kilgoreinternational.com/wp-content/uploads/2018/02/Fake-Calculus-Kit-300x300.jpg

[WM]

Am Dienstag, 12. Februar 2019 19:09:54 UTC+1 schrieb FredJeffries:
> On Tuesday, February 12, 2019 at 9:15:47 AM UTC-8, WM wrote:
> > Am Dienstag, 12. Februar 2019 18:05:42 UTC+1 schrieb FredJeffries:
> > > On Tuesday, February 12, 2019 at 8:51:13 AM UTC-8, WM wrote:
> > > > Am Dienstag, 12. Februar 2019 17:19:12 UTC+1 schrieb FredJeffries:
> > > > > On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:
> > > >
> > > > > > Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.
> > > > >
> > > > > Why should *I* attempt to "explain" such nonsensical gibberish?
> > > >
> > > > It is the essence of transfinite set theory.
> > >
> > > No, it isn't. It is gibberish promulgated by only you.
> >
> > The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]
>
> Dishonest, irrelevant misquotations. Absolutely nothing there about "McDuck's bankrupt" or "Binary Tree with aleph_0 nodes" or "aleph_0 separators of irrational numbers"...

Are you really too stupid to understand that Tristram Shandy and McDuck and the enumeration of all fractions are similar examples?

>
>
> > To have an example with a simpler ratio consider Scrooge McDuck who per day earns 10 $ and spends 1 $. The dollar bills are enumerated by the natural numbers. McDuck receives and spends them in natural order. If he lived forever he would go bankrupt. (Using coins he would get rich.)
>
>
> Your imaginary friend McDuck never GOES bankrupt

In a sequence we have a continuity of steps. If McDuck is bankrupt at some time, then he must have gone bankrupt before. We do not believe in wonders in mathematics.

Regards, WM

[j4n bur53]

Still struggling with limit? The limit is not necessarely
some element of the sequence. So your argument is

pretty baseless Volkswagen Omlette nonsense from
Augsburg Crank institute. Also McDuck and Tristram

Shandy is baseless nonsense.

[FredJeffries]

On Tuesday, February 12, 2019 at 11:01:47 AM UTC-8, WM wrote:
> Am Dienstag, 12. Februar 2019 19:09:54 UTC+1 schrieb FredJeffries:
> > On Tuesday, February 12, 2019 at 9:15:47 AM UTC-8, WM wrote:
> > > Am Dienstag, 12. Februar 2019 18:05:42 UTC+1 schrieb FredJeffries:
> > > > On Tuesday, February 12, 2019 at 8:51:13 AM UTC-8, WM wrote:
> > > > > Am Dienstag, 12. Februar 2019 17:19:12 UTC+1 schrieb FredJeffries:
> > > > > > On Monday, February 11, 2019 at 5:55:08 AM UTC-8, transf...@gmail.com wrote:
> > > > >
> > > > > > > Still waiting for you to explain McDuck's bankrupt. Or the Binary Tree with aleph_0 nodes, i.e., start ups of distinguishable paths, but uncountably many Ends of paths. Or aleph_0 separators of irrational numbers on the real axis, but uncountably many separated irrational numbers.
> > > > > >
> > > > > > Why should *I* attempt to "explain" such nonsensical gibberish?
> > > > >
> > > > > It is the essence of transfinite set theory.
> > > >
> > > > No, it isn't. It is gibberish promulgated by only you.
> > >
> > > The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]
> >
> > Dishonest, irrelevant misquotations. Absolutely nothing there about "McDuck's bankrupt" or "Binary Tree with aleph_0 nodes" or "aleph_0 separators of irrational numbers"...
>
> Are you really too stupid to understand that Tristram Shandy and McDuck and the enumeration of all fractions are similar examples?

Yes, I am too stupid to see the similarity between Fraenkel's "Tristam Shandy" and your gibberish about "McDuck" and "the enumeration of all fractions"

> > > To have an example with a simpler ratio consider Scrooge McDuck who per day earns 10 $ and spends 1 $. The dollar bills are enumerated by the natural numbers. McDuck receives and spends them in natural order. If he lived forever he would go bankrupt. (Using coins he would get rich.)
> >
> >
> > Your imaginary friend McDuck never GOES bankrupt
>
> In a sequence we have a continuity of steps. If McDuck is bankrupt at some time, then he must have gone bankrupt before.

McDuck is never "bankrupt" at any "time".

[WM]

Am Dienstag, 12. Februar 2019 21:12:50 UTC+1 schrieb FredJeffries:
> On Tuesday, February 12, 2019 at 11:01:47 AM UTC-8, WM wrote:


> > > > The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]
> > >
> > > Dishonest, irrelevant misquotations. Absolutely nothing there about "McDuck's bankrupt" or "Binary Tree with aleph_0 nodes" or "aleph_0 separators of irrational numbers"...
> >
> > Are you really too stupid to understand that Tristram Shandy and McDuck and the enumeration of all fractions are similar examples?
>
> Yes, I am too stupid to see the similarity between Fraenkel's "Tristam Shandy" and your gibberish about "McDuck" and "the enumeration of all fractions"

Better stupid than a liar.

>

> > In a sequence we have a continuity of steps. If McDuck is bankrupt at some time, then he must have gone bankrupt before.
>
> McDuck is never "bankrupt" at any "time".

Then Tristram Shandy is never ready and the rational numbers are never enumerated.

Regards, WM

[WM]

Am Dienstag, 12. Februar 2019 20:46:32 UTC+1 schrieb j4n bur53:


> Shandy is baseless nonsense.

Yes, like finished infinity and transfinite set theory.

Regards, WM

[Chris M. Thomasson]

Sorry for not totally remembering the McDuck scenario but at what
iteration would it become bankrupt? Impossible? Something about:

receiving 10 $ per day and spending 1 $ per day

One would have a 9 dollar profit per day that rolls over, he keeps the
profits. How can he go bankrupt?

[FredJeffries]

On Tuesday, February 12, 2019 at 1:29:12 PM UTC-8, WM wrote:
> Am Dienstag, 12. Februar 2019 21:12:50 UTC+1 schrieb FredJeffries:
> > On Tuesday, February 12, 2019 at 11:01:47 AM UTC-8, WM wrote:
>
>
> > > > > The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]
> > > >
> > > > Dishonest, irrelevant misquotations. Absolutely nothing there about "McDuck's bankrupt" or "Binary Tree with aleph_0 nodes" or "aleph_0 separators of irrational numbers"...
> > >
> > > Are you really too stupid to understand that Tristram Shandy and McDuck and the enumeration of all fractions are similar examples?
> >
> > Yes, I am too stupid to see the similarity between Fraenkel's "Tristam Shandy" and your gibberish about "McDuck" and "the enumeration of all fractions"
>
> Better stupid than a liar.

Since you are both, I defer to your judgement

[FredJeffries]

On Tuesday, February 12, 2019 at 1:38:21 PM UTC-8, Chris M. Thomasson wrote:
>
> Sorry for not totally remembering the McDuck scenario but at what
> iteration would it become bankrupt? Impossible? Something about:
>
> receiving 10 $ per day and spending 1 $ per day
>
> One would have a 9 dollar profit per day that rolls over, he keeps the
> profits. How can he go bankrupt?

He doesn't GO bankrupt (extreme emphasis on "go").

IF the bills are indexed by the positive natural numbers and IF on day number i he receives bills numbered 10i-9, 10i-8, ..., 10i and spends bill number i, then all you can say is that for any positive natural number k, there is a day when he will have spent bill number k and for any n > k, he will not possess bill k on day n.

[Python]

Doktor Frankenheim wrote:
> Am Dienstag, 12. Februar 2019 21:12:50 UTC+1 schrieb FredJeffries:

...

>> Yes, I am too stupid to see the similarity between Fraenkel's "Tristam Shandy" and your gibberish about "McDuck" and "the enumeration of all fractions"
>
> Better stupid than a liar.

You are both, Herr Mueckenheim.

[j4n bur53]

In set theory there is no inference rule:

forall n in N P(n) => P(N)

So what happens in eternity to a McDuck or Tristram
Shandy is up to how you define it.

And in eternity arithmetic laws dont hold anymore.
Like for example |omega+n| = |omega|.

This is basically what you can read off from Cantor
if you would study his cardinal and ordinal arithmetic.

[WM]

Am Mittwoch, 13. Februar 2019 02:54:36 UTC+1 schrieb j4n bur53:
> In set theory there is no inference rule:
>
> forall n in N P(n) => P(N)
>
> So what happens in eternity to a McDuck or Tristram
> Shandy is up to how you define it.

Set theory needs more, namely the belief that there is an instance where all his bills are spent such that none is remaining. Only then equiumerosity of received and issued bills is proven. That is the basic requirement.

Compare the Binary Tree: Set theory claims that there is an instance where uncountably many paths have separated from each other.

Regards, WM

[WM]

Am Dienstag, 12. Februar 2019 23:04:13 UTC+1 schrieb FredJeffries:


> IF the bills are indexed by the positive natural numbers and IF on day number i he receives bills numbered 10i-9, 10i-8, ..., 10i and spends bill number i, then all you can say is that for any positive natural number k, there is a day when he will have spent bill number k and for any n > k, he will not possess bill k on day n.

Trying to deceive again?

Set theory needs more, namely the belief that there is an instance where all his bills are spent such that none is remaining. Only then equiumerosity of received and issued bills is proven.

[WM]

Am Dienstag, 12. Februar 2019 22:38:21 UTC+1 schrieb Chris M. Thomasson:
> On 2/12/2019 1:29 PM, WM wrote:

> >>>>> The belief in the possibility to finish infinite bijections raises the paradoxical result that Adolf A. Fraenkel explained by Laurence Sterne's novel "The life and opinions of Tristram Shandy, gentleman". [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)] "Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long (for instance a countable infinity of years), then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]

> Sorry for not totally remembering the McDuck scenario but at what
> iteration would it become bankrupt? Impossible? Something about:
>
> receiving 10 $ per day and spending 1 $ per day
>
> One would have a 9 dollar profit per day that rolls over, he keeps the
> profits. How can he go bankrupt?

In set theory he gets bankrupt, i.e., he issues all his dollars like Tristram Shandy (see above) writes all his days. If this is not assumed, then also the batural numbers cannot finish the enumeration of the fractions either. Then set theory is dead. (Of course set theory is dead and never has been of any use, but if this becomes officially recognized, then all experts of set theory turn out to be no experts any longer.)

Regards, WM

[j4n bur53]

Nope. Believe is something from pyschology.
Math doesn't deal with believes.

"Belief is the state of mind in which a person thinks
something to be the case regardless of empirical
evidence to prove that something is the case with
factual certainty."
https://en.wikipedia.org/wiki/Belief

A theory is not a state of mind. A theory
should be communicable, and can be written
down on paper.

For example ZFC has the axiom of infinity.
Which implies the existence of at least
one inductive set.

If you don't want to use ZFC, use something
else. But to find an inconsistency in ZFC,
you need to produce a finite formula A,

and two finite proofs:

ZFC |- A

ZFC |- ~A

[Jew Lover]

On Tuesday, 12 February 2019 11:51:32 UTC-5, WM wrote:
> Am Montag, 11. Februar 2019 21:39:48 UTC+1 schrieb Jew Lover:
> > On Monday, 11 February 2019 13:10:47 UTC-5, WM wrote:
> > > Am Montag, 11. Februar 2019 17:40:11 UTC+1 schrieb Jew Lover:
>
>
> > > > > I did not claim that. Are you really a friend of logic? I claim that infinite digit sequences without finite definitions cannot determine real numbers.
> > > >
> > > > Neither can formulas.

> > >
> > > Take the finite formula: "0.111 and so on in infinity".
> >
> > > Every one can find every desired digit. But if there are arbitrarily many digits (there is never a last one) then you cannot find out how to continue.
> >

> > Not so. The sequence 0.111... is a consequence of trying to measure a rational number in base 10, that is, 1/9.
>
> Of course. 1/9 is that real number that is approached closer and closer. But the sequence has afinite definition.
> >
> > But I don't see how this is relevant? I am saying that you cannot define an incommensurable number using a formula
>
> I can, for instance by SUM (1/n!). But my claim is that without a finite formula no real number can be defined by a digit sequence.

IF it can't be defined by a digit sequence, THEN it can't be defined by a formula because a formula produces a digit sequence.

They are the SAME thing! For any formula, you can only produce a finite number of digits.

>
> Regards, WM

[j4n bur53]

WM wrote: "In set theory he gets bankrupt"
Now thats a believe. There is no proof of
that, there is no inference rule in set theory:

forall n in N P(n) => P(N)

If you have a process s1, s2, s3, ... then
this process says nothing about somega. Thats
your believe WM, where you always go wrong.

If you **set**:

somega = lim n->oo sn

then you have defined the process in
some way to continue.

But this is not part of set theory,
this is a "believe" of yours, since
it is a state of mind of your crank

brain. If you would instead write it
down as an additional axiom, it became
math again.

[j4n bur53]

The Limit Operator is not an Operator that
you can apply to any sequence and get always
something meaningful.

The Limit Operator is not what gives you
in set theory infinity from something finite
always automatically.

Thats just Nonsense "Belief" from Augsburg
Crank instituate based on Volkswagen Omellette.
In calculus and geometry, the Limit

has sometimes a meaningful meaning. Also many
notations are simply defined as limit, for
example this notation is defined as limit:

0.333...

But you cannot use it to extend finite processs
s1, s2, ... into new process steps that are
beyond those process steps n < omega,

and then invent some states somega, and expect
that this is meaningful to you. Since there is
no inference rule:

/* WMs Grand False Belief */

forall n in N P(n) => P(N)

Such a "Belief", when explicated as an axiom
would say that for every predicate where we
only know the n < omega truth values, if these

truth values are all true, then the predicate
needs also be true for omega itself. There
is no such axiom or inference rule in

FOL=+ZFC. Why should this be the case? An
arbitrary predicate can still be false at omega,
even if it is true for all n. Simplest example:

P(x) :<=> ~n = N

You have:

forall n in N P(n)

but you dont have:

~P(N)

So in general there is no inference rule:

/* WMs Grand False Belief */

forall n in N P(n) => P(N)