28 June 2022: New visitors to sci.math: The New Calculus is the first rigorous formulation in history.

[Eram semper recta]

First learn how my historic geometric identity of January 2020 proves your mainstream formulation
of calculus is an elaborate fraud:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

Seeing is believing, so download the following applet and watch how my historic geometric theorem
works for any given function:

https://drive.google.com/file/d/1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv

There are no viruses or spy software in my applets and to my knowledge most browsers will warn
you before you download any malicious code in applets. Don't waste your time on the fraudulent
mainstream formulation of calculus which cannot be understood because it is anti-mathematical nonsense.
Download my applet now and gain understanding and knowledge you couldn't find at school or university!

Second, learn how it fixes the mainstream bogus definition of definite integral:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

Applet which explains the definite integral without any ill-formed concepts such as infinity,
infinitesimals or the circular rot of limit theory:

https://drive.google.com/file/d/1JYRxjGb3MxlYWp_2KqVXwXNr5XUvUNz7

A video explaining the new applet:

https://youtu.be/TJqvbshIGtg

Third, study my free eBook because not only your mathematical future depends on it but also your sanity!

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO

Lastly, ignore all the trolls and cranks such as Dan Christensen, Jean Pierre Messager (aka Python aka YBM aka JPM),
Jan Burse, Michael MORONey, QB, Earle, Jens Stuckelberger, Jan Bilawski, Zelos Malum, Markus Klyver, Alan McKenzie,
Ludwig Poehlman (certified crank aka Archimedes Plutonium) etc. These fools have nothing to say about my work.
All they know is how to throw shade because they are ignorant, arrogant, incompetent and incorrigibly stupid.
Unfortunately, sci.math has become the mainstream's "Truth Network" - replete with paid trolls, some of whose names
are mentioned in this paragraph. These fools have lost the privilege of being educated by me. Gracing them with any
kind of response is like placing a prized pearl on a pile of dung.

I shall not respond to any of them again.

At times it's good to laugh at the stupidity and dishonesty of mainstream academics. However, the situation is dire
when religion trumps common sense:

https://drive.google.com/file/d/1520NjhgiakcrssQxtbxRCDXus_aHXpI9

This comment will be periodically reposted for the sake of new visitors as long as I am alive.

My lecture on the true Foundations of Mathematics was recorded.

You can download it here:

https://youtu.be/_WZJY1xgJTk

The Gift applet (almost in power point format!):

https://drive.google.com/file/d/1SYT-MbYtXUAYgwPeTgZ8QC8gxNpj-fap

Remember, you cannot understand mathematics without me because no one understands mathematics as
well as I do. The lecture is a bit on the slow side (because of my health issues), BUT you will
learn more about the foundations of mathematics than you ever knew your entire life!

The Elements is not about geometry. It's not about algebra. It's not about constructions. It is a
template for the realisation of all SCIENCE.

I quote a Greek scholar (http://www.physics.ntua.gr/mourmouras/euclid/common/anti_prologou.html):

Τα Στοιχεία Ευκλείδου δέν είναι Γεωμετρία (ούτε επιπεδομετρία, ούτε γεωμετρία χώρου), απλώς μπορούν
να παραχθούν από αύτα «Γεωμετρίες» (είτε «Ευκλείδειες,» είτε «μή Ευκλείδειες», κλπ), όπως επίσης
μπορούν να παραχθούν πολλές άλλες θεωρίες «Μαθηματικές» καί όχι μόνο, π.χ. Θεωρία Αριθμών, Aναλογίες,
Aσύμμετρα Μεγέθη, Θεωρία της Σχετικότητας, κ.α.

Τα Στοιχεία τού Ευκλείδου δεν είναι ούτε αντικείμενα του Πραγματικού κόσμου, καίούτε είναι αντικείμενα
τών Μαθηματικών, αλλά χωρίς αυτά, όλα τά παραπάνω δέν μπορούν να περιγραφούν, να κατανοηθούν, να ερμηνευτούν.

Πολλοί συγχέουν τον πραγματικό χώρο τών «Φυσικών» επιστημών με τά Στοιχεία Ευκλείδου. Aπό τα Στοιχεία
Ευκλείδου προέρχονται οί πλείστες μαθηματικές καί φυσικές επιστήμες, τόσο οί παραδοσιακές όσο καί οί
μοντέρνες. Γιά τις τεχνολογίες αυτό είναι προφανές.

Τα Στοιχεία Ευκλείδου αποτελούν ένα ενιαίον όλο, ένα «Σύστημα», τό οποίο είναι «κλειστό καί ἀνοικτό»,
τόσο όσο καί ή σκέψη, ό λόγος καί ή γραμματική τής ανθρώπινης υπόστασης. H πληρότητα καί ἡ συνέπεια
είναι δομημένες μέ έναν εκπληκτικό τρόπο, πού τό καθιστούν μοναδικό.

My καθαρεύουσα (high Greek) Greek is very poor, but here is my translation:

Euclidean Elements are not Geometry (neither plane geometry nor space geometry), from these can be produced
"Geometries" (either "Euclidean" or "non-Euclidean", etc.), as well as many other "Mathematical" theories
can be produced and not only, e.g. Number Theory, Proportions, Asymmetric Sizes, Theory of Relativity, etc.

The Elements of Euclid are neither objects of the real world, nor are they objects of Mathematics, but without
them, all the above cannot be described, understood, interpreted. Many confuse the real world of the "Natural"
sciences with the Euclidean Elements. Most of the mathematical and natural sciences, both traditional and modern,
come from the Euclidean Elements. For technologies this is obvious.

The Euclidean Elements constitute a single whole, a "System", which is "closed and open", as much as the thought,
reason and grammar of the human condition. Completeness and consistency are structured in an amazing way,
which make it unique.

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

This professor (of Physics and mathematics) also reads all the Ancient texts and gives lectures. He is quite an
interesting academic and very learned. He is currently reading all of Aristotle's texts:

https://www.youtube.com/c/DimitriosMourmouras

What you probably do not know is that there is no mention of any of the following words in the Elements:

axiom
geometry
straight-edge or ruler
compass

The diagrams are merely used as a means of communicating the relationships between points (location) and
distances (lines).

The Elements is a product of pure thought that was realised first by the brilliant Ancient Greeks.

Become a subscriber to my New Calculus YT channel to learn more mathematics than you learned in all your
school and university years:

https://www.youtube.com/c/JohnGabriel/videos

Mainstream mathematics has turned into a universe of alternate "facts". The majority of mainstream academics
are stupid and ignorant beyond belief so that mainstream math is today more of a cult than the science it was meant to be.

Unfortunately mainstream academia does not teach one how to think, only to memorise the prescribed doctrines
that form their official statement of beliefs. Free yourself from the utter bullshit you are forced to memorise
and if you're honest with yourself, will admit that you never actually understand.

Mainstream academia are themselves alarmed because their days of deception are numbered. I am their prime target
because the more I publish facts (truth), the more I am hated for it. Even the certified cranks (Archimedes Plutonium aka Ludwig Poehlman)
join in the mocking spectacle.

Don't believe a word I say, but prove that what I say is indeed the case. How, you ask? Use your brain!

There's more....

Learn about the BIG LIE "Calculus was made rigorous...":

https://www.academia.edu/45408445/Big_Lie_Calculus_was_made_rigorous

"Why can’t you understand the difference between assuming that f'(x)=3x^2, as a “fact” upon which to build
further proofs, and hypothesizing that f'(x) might equal 3x^2, as a guess to be treated with extreme suspicion
and checked using the definition before I’m allowed to write f'(x)=3x^2?" - Anders Kaesorg.

The 5 Step method is outlined below and it summarises the mindset of most morons from MIT:

1. Assumption of fact
2. Hypothesis
3. Probability
4. Suspicion
5. Verification

:-)

https://youtu.be/gX5Bt8BEdNM

Subscribe to my YT Channel - the best math channel on the web:

https://www.youtube.com/c/JohnGabriel/videos

Who gave you the 0.999... and the 0.333...:

Euler wrote a very good book on algebra but unfortunately it was soiled with his delusional notions.

Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1 - a + aa -aaa + ...&c.

Therefore is our fraction 1/(1+a) equal to this infinite series 1 - a + aa -aaa + ...&c.

1/(1+a) is the <<limit>> of the series <<1 - a + aa -aaa + ...&c.>>

Ergo, Lim S = S or S = Lim S.

There is much more in the following link:

https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

Free your mind from the religious rot of mainstream mathematics academia which is a full-blown cult, not
too different from that of Trump's supporters.

Learn about how dishonest and incompetent mainstream academics failed to realise a rigorous formulation of calculus:

I am a genius who discovered the New Calculus and quite possibly the greatest mathematician of all time.
If you said this, no doubt you are a crank, but I am the exception. Don't believe me?

Study my works:

My historic geometric theorem which placed the final nail in the coffin of your bogus mainstream formulation of calculus:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

It's demonstrated for any smooth function in this free applet:

https://drive.google.com/file/d/1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv

Greek language applet:

https://drive.google.com/file/d/120g3VfFFqAzyZWHzHljXZYuWYpl5kUDB

How the theorem fixes your bogus mainstream formulation using Newton's and Leibniz's juvenile ideas:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

Definite integration (no hand waving circular nonsense of limit theory, infinitesimals, infinity,
Riemann sums and the myriad of mainstream shit one finds in textbooks) demonstrated for any smooth
function in this free applet:

https://drive.google.com/file/d/1JYRxjGb3MxlYWp_2KqVXwXNr5XUvUNz7

Greek language applet:

https://drive.google.com/file/d/1iG5Oc7pV3x3AIVcz6Cpd4x5UavYMwhhp

Explaining my historic identity:

https://drive.google.com/file/d/1sjs3eZJZnwI6caaUA1MtC7FhNYSLfICZ

You won't find this information anywhere else! I offer it free of charge to you.

Today I am the greatest mathematician. If history is written correctly, I will be remembered as the greatest
mathematician ever.

It will be your loss if you pass on this once in a lifetime opportunity.

Learn about my first contact with your bullshit mainstream calculus:

I first made contact with the flawed mainstream formulation of calculus in the encyclopedia Britannica. It was
on page 600 of that edition. In the following article I give you a glimpse into my genius mind and share some
of my thoughts with lesser mortals such as you.

https://www.academia.edu/61998111/My_First_Contact_with_the_flawed_mainstream_calculus

Some excerpts:

As you can see, it was called the “Calculus of Differences”, which is somewhat of a misnomer. This raised the
first red flag in my mind. It’s not as if the “Calculus of Variations” is a different kind of calculus at all.
The latter is optimisation using calculus. Karen Uhlenbeck(who in her silly Abel prize winner speech claimed
that it is not just about optimisation clearly never understood calculus), the Abel prize laureate was recognised
for her “work” in this respect. So, both these expressions are extraneous verbiage. The name is simply “Calculus”.


For starters, the mainstream morons of math academia(BIG STUPID incorrigible apes) obfuscated these definitions
even further while claiming they had rigorised calculus. The use of omega (w) was dropped for h.
Next, they added the flawed concept of limit, not realising that the expression called a finite difference is
stated as an equation using my historic geometric identity of January2020:

[ f(x+h)-f(x) ] / h = f'(x) + Q(x,h)

In effect, what the buffoons of mainstream math academia had done was to take the limit of a constant, ie, Q(x,h),
which even in their theory cannot change, but in the limit definition, it goes to ZERO!

If it is not zero, the RHS is no longer equal to the LHS. The primates reason as follows:

lim_{h->0} [ f(x+h)-f(x) ] / h = f'(x) + lim_{h->0} Q(x,h)

There are so many things wrong with what the orangutans did.

1. The limit of a constant is the constant itself.
2. They assume that only f'(x) remains constant.
3. The limit definition itself is circular, because as an MIT master graduate (an imbecile called Anders Kaesorg) once said:

"The definition of the derivative in standard calculus is f'(x) is the number m, iff it exists) such that for all
epsilon > 0, there exists a delta > 0, such that for all h =/= 0, with |h|<delta, | f(x+h)-f(x) ] / h -m | < epsilon."

Dunno about you, but isn't the derivative m used in its own definition?

m is the derivative which is used in the verifinition (portmanteau of verification and definition). In other words, this
was all magic! Chuckle.

Until my historic geometric theorem, the apes of mainstream academia had no valid systematic way of computing the
derivative, never mind the definite integral!

In another comment he was called out about claiming that h can never be zero, however, the effect of taking the limit
of the constant (mind you!) Q(x,h) is equivalent to setting h=0!

By the time I was 13 years of age, I had already taught myself the garbage of mainstream calculus. I would be modest
if I said that my knowledge of calculus at that age had already surpassed that of any mainstream professor of mathematics.


One wonders if the previous form was purposely used in an act of willful deception. The higher up the academic math ape,
the more chances are that it is a well-known fact the definition was flawed and they had no clue how to fix it. Since they
did not know, the next best thing was to pile up tons of rubbish theory such as the construction of “real numbers” which
is a fallacy since there is no valid construction. Add in the laughable ZFC axioms and who would even dare to challenge
the authenticity of their utter rot.

Then at the beginning of the twentieth century, very bad ideas such as instantaneous rate of change were introduced by
the idiots at the top Ivy League unis. One such idiot is Prof. Gilbert Strang (MIT) - a proper idiot if there ever was one.

All the mainstream academics I have encountered are incompetent, ignorant, arrogant and incorrigibly stupid. The few
that know I am right, are too cowardly to step forward and say so.

****A crank is one who cannot be convinced in the face of overwhelming evidence.****

The majority of mainstream mathematics academics are cranks or truth-deniers.

[Dan Christensen]

STUDENTS BEWARE: Don't be a victim of John Gabriel's fake math
JG's Pathetic Daily Spam Post -- Same shit AGAIN and AGAIN!


On Monday, June 27, 2022 at 11:40:43 PM UTC-4, Eram semper recta wrote:
> First learn how ...

[snip]

When will YOU learn Troll Boy?

JG here claims to have a discovered a shortcut to mastering calculus without using limits. Unfortunately for him, this means he has no workable a definition of the derivative of a function. It blows up for functions as simple f(x)=|x|. Or even f(x)=0. As a result, he has had to ban 0, negative numbers and instantaneous rates of change rendering his goofy little system quite useless.

Forget calculus. JG has also banned all axioms because he cannot even derive the most elementary results of basic arithmetic, e.g. 2+2=4. Such results require the use of axioms, so he must figure he's now off the hook.

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

[Pete]

On 6/27/2022 8:40 PM, Eram semper recta ("I am always a rectum") wrote:

> First learn how my hysteric geometric identity of January 2020 is a steaming pile of barnyard excrement.

Shut up idiot.

[Olden Yokokawa]

Dan Christensen wrote:

> On Monday, June 27, 2022 at 11:40:43 PM UTC-4, Eram semper recta wrote:
>> First learn how ... [snip]
>
> When will YOU learn Troll Boy?

former brother country to Russia. You don't want to be Bulgaria starting
the next three four months. Actually it's just the corrupt government, not
the people. Anyway. How stupid people can be, buying the empty capitalist
stinking western europe. I can't believe they are so stupid. Selling their
country to the west for empty promises. They are not even in the Schengen
territory. What a fools. Dropping your own brother for the sake of the
liberal capitalist EU terrorists.

Bulgaria expels dozens of Russian diplomats
https://www.rt.com/russia/558022-bulgaria-diplomats-expelled-intelligence/

[Dan Christensen]

On Tuesday, June 28, 2022 at 3:55:00 PM UTC-4, Olden Yokokawa wrote:
> Dan Christensen wrote:
>
> > On Monday, June 27, 2022 at 11:40:43 PM UTC-4, Eram semper recta wrote:
> >> First learn how ... [snip]
> >
> > When will YOU learn Troll Boy?
> former brother country to Russia. You don't want to be Bulgaria starting
> the next three four months. Actually it's just the corrupt government, not
> the people. Anyway. How stupid people can be, buying the empty capitalist
> stinking western europe. I can't believe they are so stupid. Selling their
> country to the west for empty promises. They are not even in the Schengen
> territory. What a fools. Dropping your own brother for the sake of the
> liberal capitalist EU terrorists.
>

The Nazi war criminal Putin lost all credibility with his genocidal war of conquest in Ukraine. His aim is clearly to punish the Ukrainian people for turfing out his corrupt puppet regime and electing a Jewish president and prime minister. There can be absolutely no excusing his bombing of homes, schools, hospitals and markets. It is beyond denying at that this point. Don't even try.

Better make your escape while you can, Nazi Boy. The Finnish border is already closed.

[Clint Ochiai]

Dan Christensen wrote:

>> Selling their country to the west for empty promises. They are not even
>> in the Schengen territory. What a fools. Dropping your own brother for
>> the sake of the liberal capitalist EU terrorists.
>>
>>

> The Nazi war criminal Putin lost all credibility with his genocidal war

> of conquest in Ukraine. He aim is clearly to punish the Ukrainian people

> for turfing out his corrupt puppet regime and electing a Jewish
> president and

not "Jewish" you fucking idiot, but a stinking khazar. If you don't know
the lying khazar, you are unable to do mathematicians. The cocaine khazar
zelenske is even marked citizen in other country. He has nothing to do
with the fake fictitious "u_kraine". He is a cocaine puppet. You fucking
braindead nazi idiot. From a Mathematics and Physics professor:

2022.06.28 The Sitzkrieg We’re In https://youtu.be/d-BzyGQ_XSg

[Mostowski Collapse]

STUDENTS BEWARE: Don't be a victim of Dan Christensens fake math
Ok, Dan Christensen, our DC Pooper, thinks this here should be provable
where f is arbitrary FOL function symbol:

ALL(x):EXIST(y):f(x) = y

So in his DC Poop logic FOL function symbols are not total on
the domain of discourse, whereas on ordinary first order logic
the above is provable.

So far so good, we can conclude DC Poop is not first order logic.

But what about this theorem, that is also sufficient for
Russells Paradox if we would put f into the domain of discourse,
is it also not provable?

EXIST(f):ALL(x):EXIST(y):f(x) = y

LMAO!

P.S.: A witness for such an f in first order logic and set theory
would be f = singleton, i.e. f(x) = {x}. In ZFC we can surely prove
ALL(x):EXIST(y):{x} = y, I guess in ZFCU as well.

[Mostowski Collapse]

Corr.: Typo

> Ok, Dan Christensen, our DC Pooper, thinks this here should

> not be provable where f is arbitrary FOL function symbol:

[Dan Christensen]

On Monday, July 4, 2022 at 8:26:40 AM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> Dan Christensen schrieb am Dienstag, 28. Juni 2022 um 20:59:37 UTC+2:
> > STUDENTS BEWARE: Don't be a victim of John Gabriel's fake math
> > JG's Pathetic Daily Spam Post -- Same shit AGAIN and AGAIN!

> STUDENTS BEWARE: Don't be a victim of Dan Christensens fake math

Awwww... So cute the way you "stick up" for your little buddy and fellow troll here, Jan Burse. A match made in heaven!

> Ok, Dan Christensen, our DC Proofer, thinks this here should be provable

> where f is arbitrary FOL function symbol:
>
> ALL(x):EXIST(y):f(x) = y
>

You would need to introduce some of your wonky axiom(s) to obtain this result, Jan Burse.

[snip]

> So far so good, we can conclude DC Proof is not first order logic.
>

Rather, it uses the rules of logic implicitly used in most math proofs in textbooks.

> But what about this theorem, that is also sufficient for
> Russells Paradox if we would put f into the domain of discourse,
> is it also not provable?
>
> EXIST(f):ALL(x):EXIST(y):f(x) = y
>

You have already failed elsewhere to obtain this result in DC Proof without introducing some of your wonky axiom(s). Do keep trying.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com

Visit my Math Blog at http://www.dcproof.wordpress.com

[Mostowski Collapse]

You only tell us that this here is not provable:

ALL(f):ALL(x):EXIST(y):f(x) = y

But what about this here:

EXIST(f):ALL(x):EXIST(y):f(x) = y

Obviously the Peano Unit, written as {x}, which is also
used in Zermelos Axiom from 1908, satisfies the above
second variant. If you take g(x) = {x}, you have in g

an existence witness for EXIST(f), since we have:

ALL(x):EXIST(y):{x}=y

Or do you deny the later. Its a consequence of the Pairing Axiom.

[Mostowski Collapse]

In ordinary FOL + ZFC you would make this definition:

ALL(x):ALL(z):[z e {x} <=> z = x]

I guess you can then show that {_} is a function using
ZFC, like extensionality and paring axiom, and that the
above is a conservative extension. Namely you should be

able to verify this criteria of conservative extension:

∀x1 … ∀xn ∃!yϕ(y, x1 , … , xn)
https://en.wikipedia.org/wiki/Extension_by_definitions#Definition_of_function_symbols

Can you prove in DC Poop the following:

∀x ∃!y ∀z (z e y <=> z = x)

Please show us....

[Mostowski Collapse]

What are you bragging about?
Are you now bat shit crazy again?

Dan Christensen schrieb am Montag, 4. Juli 2022 um 17:00:17 UTC+2:
> If you want to derive ∀x∃y f(x) = y in any formal system
> (like DC Proof), you cannot be adding new axioms to force it.

Its provable in FOL without adding new axioms:

∀x∃yf(x)=y is valid.
https://www.umsu.de/trees/#~6x~7yf%28x%29=y

Whats wrong with you?
Its a bug that its not anymore provable in DC Poop.

[Dan Christensen]

See my postings just now to your identical postings at sci.logic.

Dan

On Monday, July 4, 2022 at 5:53:05 PM UTC-4, Mostowski Collapse wrote:
> You only tell us that this here is not provable:
>
> ALL(f):ALL(x):EXIST(y):f(x) = y
>
> But what about this here:
> EXIST(f):ALL(x):EXIST(y):f(x) = y
> Obviously the Peano Unit, written as {x}, which is also

> used in Zermelos Axiom from 1908, satisfies the above ....

[snip]

[Mostowski Collapse]

Dan Christensen haluzinated:
> It is possible, however, to prove:
> ALL(a):[Set(a) => ALL(b):[b in a => EXIST(c):[Set(c) & b in c & ALL(d):[d in c <=> d=b]]]]

No, thats restricted singleton. Basically you
have something like b e a => ∃c c= {b}. But the
singleton exists unrestrictedly.

Can you get rid of b e a? The singleton derived
from pairing axiom in ZFC, by extending ZFC
conservatively by the function symbol {_}:

ALL(x):EXIST(y):{x}=y

Unrestricted, for every x there is such an y.
For every x, we do not need to know whether x is
some member of some set.

You can check yourself:

∀ A ∀ B ∃ C ∀ D [ D ∈ C ⟺ ( D = A ∨ D = B ) ]
https://en.wikipedia.org/wiki/Axiom_of_pairing

There is no nonsense of your quantifier restriction
that we see all over the place. Got it?

[Dan Christensen]

On Tuesday, July 5, 2022 at 9:09:41 AM UTC-4, Mostowski Collapse wrote:
> Dan Christensen haluzinated:
> > It is possible, however, to prove:
> > ALL(a):[Set(a) => ALL(b):[b in a => EXIST(c):[Set(c) & b in c & ALL(d):[d in c <=> d=b]]]]
>
> No, thats restricted singleton.

In mathematical proofs, the Subset Axiom (on the Sets menu) will usually suffice. On the rare occasion that users may required a true pairing axiom, they can introduce the following axiom at the beginning of their proof using the Create Axiom rule (on the Logic menu):

1. ALL(a):ALL(b):EXIST(c):[Set(c) & ALL(d):[d in c <=> d=a | d=b]]
Axiom

For a singleton, you have a=b.

I hope this helps.

[Micah Watanabe]

Dan Christensen wrote:

> See my postings just now to your identical postings at sci.logic.

You stinking nazi, tell me this khakhole nazi wanker deserves walking on
the face of the earth. Tell those arming the fictitious "u_krainian"
khazar nazis, deserves walking on the face of the earth, likewise. In 1945
you'll be hanged in trees, by the people, for the people, you deplorable
subhuman excrement.

Ukrainian Journalist in 2014 - '1.5M people in Donbas are 'superfluous',
need to be 'exterminated'' https://www.bitchute.com/video/D1mtLSK347CQ/

[Dan Christensen]

On Tuesday, July 5, 2022 at 12:19:19 PM UTC-4, Micah Watanabe wrote:
> Dan Christensen wrote:
>
> > See my postings just now to your identical postings at sci.logic.
> You stinking nazi,

You are the one promoting a genocidal, Nazi-style war of conquest by the war criminal Putin.

Escape while you can, Nazi boy. The Finnish border is already closed. Maybe turn yourself in at the Polish border? If the trains are still running, you might go on a "shopping trip" to China, though even the Chinese authorities may take a dim view of YOUR war crimes here. But you probably won't be jailed. At worst, you might deported back to ruSSia. Worth a try?

[Jonas Tanaka]

Dan Christensen wrote:

> On Tuesday, July 5, 2022 at 12:19:19 PM UTC-4, Micah Watanabe wrote:
>> Dan Christensen wrote:
>>
>> > See my postings just now to your identical postings at sci.logic.
>> You stinking nazi,
>
> You are the one promoting a genocidal, Nazi-style war of conquest by
> the

stop deleting the recorded data, incriminating, you repugnant nazi bitch.
Admit your lies and nazism, and hope you're entitled to receive mercy.

[Dan Christensen]

On Tuesday, July 5, 2022 at 1:41:48 PM UTC-4, Jonas Tanaka wrote:
> Dan Christensen wrote:
>
> > On Tuesday, July 5, 2022 at 12:19:19 PM UTC-4, Micah Watanabe wrote:
> >> Dan Christensen wrote:
> >>
> >> > See my postings just now to your identical postings at sci.logic.
> >> You stinking nazi,
> >
> > You are the one promoting a genocidal, Nazi-style war of conquest by
> > the
> stop deleting the recorded data, incriminating, you repugnant nazi bitch.
> Admit your lies and nazism, and hope you're entitled to receive mercy.

Don't bother showing your "recorded data" to the judges at your war crimes trial, Nazi boy. It will only make matters worse for you. And don't say you were "just following orders." They won't be impressed.

[Nesti Yamura]

Dan Christensen wrote:

>> > You are the one promoting a genocidal, Nazi-style war of conquest by
>> > the
>> stop deleting the recorded data, incriminating, you repugnant nazi
>> bitch.
>> Admit your lies and nazism, and hope you're entitled to receive mercy.
>
> Don't bother showing your "recorded data" to the judges at your war

the nazi regime abusing cacanada are fucked up serioja. Stop deleting the
evidences putting you before the execution squad, you stinking lying and
deceiving son of the bitch.

Ukrainian Journalist in 2014 - '1.5M people in Donbas are 'superfluous',
need to be 'exterminated'' https://www.bitchute.com/video/D1mtLSK347CQ/

Germany is KAPUT - Why 'Germany's stealing *capitalist* Business Model Is
Actually Gone' https://www.bitchute.com/video/LGSRfYX09a3A/

[Brock Namiki]

Dan Christensen wrote:

> On Tuesday, July 5, 2022 at 9:09:41 AM UTC-4, Mostowski Collapse wrote:
>> Dan Christensen haluzinated:

>> > ALL(d):[d in c <=> d=b]]]]
>>
>> No, thats restricted singleton.
>
> In mathematical proofs, the Subset Axiom (on the Sets menu) will usually

you lying and deceiving sondre bitch.

Ukrainian Journalist in 2014 - '1.5M people in Donbas are 'superfluous',
need to be 'exterminated'' https://www.bitchute.com/video/D1mtLSK347CQ/

2022.07.05 The Netherlands Is On Fire
https://www.youtube.com/watch?v=m2HYnbs02Vs

This alien looking thing was pulled out of the body ofa dead person who
was vaccinated https://www.bitchute.com/video/ihbPpMNligNi/

Germany is KAPUT - Why 'Germany's Business Model Is Actually Gone'
https://www.bitchute.com/video/LGSRfYX09a3A/

[Laron Toru]

Mostowski Collapse wrote:
> Dan Christensen haluzinated:
>> It is possible, however, to prove:

> No, thats restricted singleton. Basically you have something like
> b e a => ∃c c= {b}. But the singleton exists unrestrictedly.

ohh really, the fake_money khakhole switzarland never been a "democracy".
It's a sondre bitch lying and deceiving shithole.

Mick Wallace, Member of the European Parliament, on US democracy
https://www.bitchute.com/video/VtcFFkafAsfx/

[Jojo Kaneko]

Dan Christensen wrote:

> See my postings just now to your identical postings at sci.logic.

wow, send more weapons to the nazi "ukraine".

Russians found another Ukrainian warehouse with abandoned American FGM-148
Javelins https://www.bitchute.com/video/a0CXXvxXlYHk/

watch these proofs. Amazing.

Russians from the 'O' group captured a Ukrainian ammo depot with lots of
125mm shells https://www.bitchute.com/video/DJy9KhmYYJsG/

IT'S OFFICIAL - Ukrainian women will be sent to fight at the front lines!
https://www.bitchute.com/video/T7lLgRFDg27X/

these nazi whores may stop *jumping_up*, wearing nazi flags, in the middle
of Vienna, Austria. It's a sin.

Ukrainians ran so fast from Lysychansk that they left their trousers
hanging out https://www.bitchute.com/video/8m3ZFuIrDUNu/

[Michael Moroney]

On 7/5/2022 2:31 PM, Nesti Yamura wrote:
> Dan Christensen wrote:
>
>>>> You are the one promoting a genocidal, Nazi-style war of conquest by
>>>> the
>>> stop deleting the recorded data, incriminating, you repugnant nazi
>>> bitch.
>>> Admit your lies and nazism, and hope you're entitled to receive mercy.
>>
>> Don't bother showing your "recorded data" to the judges at your war
>
> the nazi regime abusing cacanada are fucked up serioja. Stop deleting the
> evidences putting you before the execution squad, you stinking lying and
> deceiving son of the bitch.
>
> Ukrainian Journalist in 2014 - '1.5M people in Donbas are 'superfluous',
> need to be 'exterminated''

Wow, I knew 卐Ru⚡︎⚡︎ia卐 has been sending Ukrainians to so-called
"filtration camps", but I never knew 卐Ru⚡︎⚡︎ia卐 has been doing that
since 2014! Why does 卐Ru⚡︎⚡︎ia卐 want to exterminate 1.5 million? So
卐Putler卐 can say at his Nuremburg 2.0 trial that he wasn't as evil as
卐Hitler卐 ? Will he say "Hey, Hitler exterminated 6 million Jews, but I
exterminated only 1.5 million innocent Ukrainians!" ? Well, it
definitely won't work for him, and you'd better find some border, any
border, to cross to get out of 卐Ru⚡︎⚡︎ia卐 before it's your neck in the
noose.

[Russ Kurofuji]

Michael Moroney wrote:

>> the nazi regime abusing cacanada are fucked up serioja. Stop deleting
>> the evidences putting you before the execution squad, you stinking
>> lying and deceiving son of the bitch.
>>
>> Ukrainian Journalist in 2014 - '1.5M people in Donbas are
>> 'superfluous', need to be 'exterminated''

>> https://www.bitchute.com/video/D1mtLSK347CQ/

> Wow, I knew 卐Ru⚡︎⚡︎ia卐 has been sending Ukrainians to so-called
> "filtration camps", but I never knew 卐Ru⚡︎⚡︎ia卐 has been doing that

nobody can read the crap you post. Make it shorter and stop using
nonsensical unicode. You nazi promoter. The nazis will turn around beating
your ugly ass. They did it before. They are ready to do it right now.

the cocaine zelenske is scared like shit, right now as we speak. The nazis
to die for him and his oligarchs. They will not forget him. Btw, going to
*military* in a *capitalist* country is *crazyness*. Going to *_war_* for
a *capitalist* country makes you *_stupid_like_an_asshole_*.

Zelensky's 'crazy eyes' during his meeting with Swedish PM
https://www.bitchute.com/video/UouIoGm5TDNI/

UH-OH France24 is letting it slip that Lysychansk residents are HAPPY that
Russians have come https://www.bitchute.com/video/JR3IPSPFR8S0/