Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss

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

110 views
Skip to first unread message

Eram semper recta

unread,
May 17, 2022, 11:33:19 PM5/17/22
to
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.

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 shitting themselves because their days are numbered. I am their prime target because the more I publish facts (truth), the more I am hated for it. Even the 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 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 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 bullshit 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 baboons 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

unread,
May 18, 2022, 12:14:24 AM5/18/22
to
STUDENTS BEWARE: Don't be a victim of John Gabriel's fake math

JG's Pathetic Daily Spam Post -- It's the SAME SHIT EVERY DAY!!!

On Tuesday, May 17, 2022 at 11:33:19 PM UTC-4,I am Super Rectum (aka John Gabriel) wrote:
> First learn how ...

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

Mostowski Collapse

unread,
May 18, 2022, 7:21:40 AM5/18/22
to
STUDENTS BEWARE: Don't be a victim of Dan Christensen's fake math
He thinks this here are natural numbers:
https://dcproof.com/EvenNextOdd.htm

But he cannot prove:
~EXIST(a):[a e n & a < 0]

LoL

Dan Christensen

unread,
May 18, 2022, 9:41:47 AM5/18/22
to
On Wednesday, May 18, 2022 at 7:21:40 AM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:

"Sticking up" for your little buddy and fellow troll as always, Jan Burse? (Wink, wink!)

> STUDENTS BEWARE: Don't be a victim of Dan Christensen's fake math
> He thinks this here are natural numbers:
> https://dcproof.com/EvenNextOdd.htm
>

There, from a list of results from basic arithmetic on N (lines 1-14) and a standard definition of EVEN and ODD (lines 15-16), I was able to formally derive:

ALL(a):[a e n => [Even(a) => Odd(a+1)]]

ALL(a):[a e n => Even(2*a) & Odd(2*a+1)]

where n = the set of natural numbers.

Not even Jan Burse here can deny it.

> But he cannot prove:
> ~EXIST(a):[a e n & a < 0]
>

Another lie.

Poor Jan Burse still doesn't get it. He believes that it is possible to make logical inferences about functions outside of their domains of definition, i.e. where they are technically UNDEFINED! Some nonsense about "dark elements?"

Dan

Alto Handa

unread,
May 18, 2022, 2:18:46 PM5/18/22
to
Dan Christensen wrote:

> On Wednesday, May 18, 2022 at 7:21:40 AM UTC-4, Mostowski Collapse (aka
> Jan Burse) wrote:
>
> "Sticking up" for your little buddy and fellow troll as always, Jan
> Burse?
> (Wink, wink!)

so true

Derek Otaka

unread,
May 18, 2022, 2:45:17 PM5/18/22
to
Dan Christensen wrote:

> On Tuesday, May 17, 2022 at 11:33:19 PM UTC-4,I am Super Rectum (aka John
> Gabriel) wrote:
>> First learn how ...

Mitchell Center Podcast: Naming the Problem: Capitalism is the Crisis
Richard Wolff
https://www.rdwolff.com/mitchell_center_podcast_naming_the_problem_capitalism_is_the_crisis

Mostowski Collapse

unread,
May 21, 2022, 6:02:12 PM5/21/22
to
It depends. In your file EvenNextOdd.htm, you should
write the following:

6 ALL(a):ALL(b):[a e d & b e d => a+b e d]
Axiom
Properties of +
7 ALL(a):ALL(b):[a e d & b e d => a+b=b+a]
Axiom
https://dcproof.com/EvenNextOdd.htm

Where is associativity? LoL
Where is all of Peano? LMAO!
Do you see the problem, or are you just too dumb?

You should not write n, if its not n. No mathematician
does that. Your axioms define some structure <D, +, ...>
but its not necessarely the structure <N, +, ...>

So the correct offending theorem would be anyway:

ALL(a):[a e d => [a < 0 => ~Odd(a)]]

Which makes it even more clear why its not provable.

Dan Christensen

unread,
May 21, 2022, 11:26:26 PM5/21/22
to
On Saturday, May 21, 2022 at 6:02:12 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> It depends. In your file EvenNextOdd.htm, you should
> write the following:
>
> 6 ALL(a):ALL(b):[a e d & b e d => a+b e d]
> Axiom

Wrong again, Troll Boy. It is correctly stated as:

ALL(a):ALL(b):[a e n & b e n => a+b e n]

where n = the set of natural numbers.

> Properties of +
> 7 ALL(a):ALL(b):[a e d & b e d => a+b=b+a]
> Axiom
> https://dcproof.com/EvenNextOdd.htm
>
> Where is associativity? LoL

Not required in the proof. Geez yer dumb. Learn some math.

> Where is all of Peano? LMAO!

Likewise, not required, idiot!

> So the correct offending theorem would be anyway:
>
> ALL(a):[a e d => [a < 0 => ~Odd(a)]]
>

Wrong again, Troll Boy. This, too, was not required. In any case, it would be correctly stated as:

ALL(a):[a e n => [a < 0 => ~Odd(a)]]

Geez, you really are dumb, Jan Burse.

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

unread,
May 22, 2022, 4:32:56 AM5/22/22
to
If only your axioms would exactly capture n. But this is not
what they do. You cannot prove from your nonsense axioms:

ALL(a):ALL(b):[a e n & b e n => [Even(a) & Even(b) => Even(a+b)]]
ALL(a):ALL(b):[a e n & b e n => [Even(a) & Odd(b) => Odd(a+b)]]
ALL(a):ALL(b):[a e n & b e n => [Odd(a) & Even(b) => Odd(a+b)]]
ALL(a):ALL(b):[a e n & b e n => [Odd(a) & Odd(b) => Even(a+b)]]

Mostowski Collapse

unread,
May 28, 2022, 3:53:38 PM5/28/22
to
What errors? I consider this rather a feature than a bug:

Dan Christensen schrieb am Montag, 9. Mai 2022 um 06:11:47 UTC+2:
> Even(-1), however, will be UNDEFINED in case 1, but FALSE in case 2.
https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/1WIQ11zEAQAJ

I guess most people will agree that Even(-1) should be
false when Even has the meaning even natural number.
Or do you claim that -1 e {0,2,4,...} is UNDEFINED?

LoL

Maybe make a John Garbiel and Dan Christensen combined
list. Put some John Garbiel into the list, and some Dan Christensen
in the list, here is a fresh addition for Dan Christensen:

"Even(-1), however, will be UNDEFINED in case 1"
- 9. Mai 2022 (Dan Christensen)

Mostowski Collapse

unread,
May 28, 2022, 5:08:21 PM5/28/22
to
Well the list is longer:

"Even(-1), however, will be UNDEFINED in case 1"
- 9. Mai 2022 (Dan Christensen)

For Even(2) we need more axioms
- 27. Mai 2022 (Dan Christensen)

Which is quite cringe since the Pressburger definition of
Even is quite powerful, here some Prolog:

add(0, X, X).
add(s(X), Y, s(Z)) :- add(X, Y, Z).

even(X) :- add(Y,Y,X).

The thingy terminates always:

?- even(s(s(s(s(0))))).
true ;
false.

?- even(s(s(s(s(s(0)))))).
false.

Woa!

Dan Christensen

unread,
May 28, 2022, 5:52:16 PM5/28/22
to
On Saturday, May 28, 2022 at 3:53:38 PM UTC-4, Mostowski Collapse wrote:
> What errors?

Your bizarre belief that you can make logical inferences about functions and predicates outside of their domains of definitions, i.e. where they are undefined.

Dan

Reid Kubota

unread,
May 28, 2022, 5:53:26 PM5/28/22
to
Mostowski Collapse wrote:

> Well the list is longer:
>
> "Even(-1), however, will be UNDEFINED in case 1"
> - 9. Mai 2022 (Dan Christensen)
>
> For Even(2) we need more axioms - 27. Mai 2022 (Dan Christensen)

this is incorrect.

Hayse Soho

unread,
May 28, 2022, 5:58:42 PM5/28/22
to
absolutely.

Dan Christensen

unread,
May 28, 2022, 6:00:25 PM5/28/22
to
On Saturday, May 28, 2022 at 5:08:21 PM UTC-4, Mostowski Collapse wrote:
> Well the list is longer:
> "Even(-1), however, will be UNDEFINED in case 1"

There you go again with your "dark elements." Maybe you should also team up with your fellow troll WM on this.

> - 9. Mai 2022 (Dan Christensen)
> For Even(2) we need more axioms

Nope, you just need some basic arithmetic, e.g. 2*1=2. Didn't they teach you that in school?

> - 27. Mai 2022 (Dan Christensen)
>
> Which is quite cringe since the Pressburger definition of
> Even is quite powerful, here some Prolog:
>

Poor Jan Burse just can't seem to get the hang of Peano's Axioms (like his little buddy and fellow troll JG), so he is forced to cast about in Presburger arithmetic and Prolog -- obvious dead ends here.

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

unread,
May 28, 2022, 6:11:22 PM5/28/22
to
Presburger Arithmetic ⊆ Peano Arithmetic

Or more precisely:

Presburger Arithmetic = Peano Arithmetic \ Multiplication

Whats wrong with you? You don't need Multiplication for Even:

Even(x) = EXIST(y): y + y = x

So why introduce Multiplication. Doesn't make any sense.

Dan Christensen

unread,
May 28, 2022, 7:36:52 PM5/28/22
to
On Saturday, May 28, 2022 at 6:11:22 PM UTC-4, Mostowski Collapse wrote:
> Presburger Arithmetic ⊆ Peano Arithmetic
>
> Or more precisely:
>
> Presburger Arithmetic = Peano Arithmetic \ Multiplication
>

Maybe you didn't know, but multiplication is really quite important in mathematics. (HA, HA, HA!!!)

Dan

Mostowski Collapse

unread,
May 28, 2022, 7:43:06 PM5/28/22
to

You dont need it to define Even.
Whats wrong with you?

Dan Christensen

unread,
May 28, 2022, 9:31:45 PM5/28/22
to
On Saturday, May 28, 2022 at 7:43:06 PM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Sonntag, 29. Mai 2022 um 01:36:52 UTC+2:
> > On Saturday, May 28, 2022 at 6:11:22 PM UTC-4, Mostowski Collapse wrote:
> > > Presburger Arithmetic ⊆ Peano Arithmetic
> > >
> > > Or more precisely:
> > >
> > > Presburger Arithmetic = Peano Arithmetic \ Multiplication
> > >
> > Maybe you didn't know, but multiplication is really quite important in mathematics. (HA, HA, HA!!!)
> >

> You dont need it to define Even.

So what? You will need multiplication for other applications. Jeez yer dumb, Jan Burse!

Dan

Mostowski Collapse

unread,
May 29, 2022, 2:51:19 AM5/29/22
to
STUDENTS BEWARE: Don't be a victim of Dan Christensen's fake math
he is ingeniously troubled by defining Even={0,2,4,...}, so far we have:

"Even(-1), however, will be UNDEFINED in case 1"
- 9. Mai 2022 (Dan Christensen)

For Even(2) we need more axioms/theorems
- 27. Mai 2022 (Dan Christensen)

A total failure so far. LoL

Dan Christensen

unread,
May 29, 2022, 11:34:36 AM5/29/22
to
On Sunday, May 29, 2022 at 2:51:19 AM UTC-4, Mostowski Collapse wrote:
> STUDENTS BEWARE: Don't be a victim of Dan Christensen's fake math
> he is ingeniously troubled by defining Even={0,2,4,...}, so far we have:
> "Even(-1), however, will be UNDEFINED in case 1"
> - 9. Mai 2022 (Dan Christensen)

Usually, an evenness predicate would be defined only on the natural numbers. But you are free to introduce your own wonky definition in DC Proof and define it for every object in the universe -- your "dark elements."

> For Even(2) we need more axioms/theorems
> - 27. Mai 2022 (Dan Christensen)
>

Yes, you would also need the "theorem" 2*1=2, which is derivable from Peano's Axioms, as are the required results of basic arithmetic on lines 1-14.
https://dcproof.com/EvenNextOdd.htm

> A total failure so far. LoL

Your theory of "dark elements" (?) would seem to be total failure, Jan Burse. Deal with it.

Mostowski Collapse

unread,
May 29, 2022, 3:03:58 PM5/29/22
to
Because your nonsense has among its models, in a model where a*b=0:
Even={0}
Odd={1,2,3,..}

You can only prove:
ALL(a):[a e n => [Even(a) => Odd(a+1)]]
https://dcproof.com/EvenNextOdd.htm

But you cannot prove, the above model is counter model:
ALL(a):[a e n => [Even(a) => Even(a+2)]]
ALL(a):[a e n => [Odd(a) => Even(a+1)]]

Means you cannot verify these two variants:

Variant I:
Even(0).
Even(s(s(x))) <= Even(x)
The smallest such Even
Odd(s(x)) <= Even(x)
The smallest such Odd

Variant II:
Even(0).
Even(s(x)) <= Odd(x)
Odd(s(x)) <= Even(x)
The smallest such Even/Odd
https://coq.inria.fr/library/Coq.Arith.Even.html

Dan Christensen

unread,
May 29, 2022, 3:31:56 PM5/29/22
to
On Sunday, May 29, 2022 at 3:03:58 PM UTC-4, Mostowski Collapse wrote:
> Because your nonsense has among its models, in a model where a*b=0:
> Even={0}
> Odd={1,2,3,..}
>

Pay attention, Jan Burse! We have:

Even={0, 2, 4, 6, ... }
Odd={1, 3, 5, 7, ... }

> You can only prove:
> ALL(a):[a e n => [Even(a) => Odd(a+1)]]

Also:
ALL(a):[a e n => Even(2*a) & Odd(2*a+1)]

> https://dcproof.com/EvenNextOdd.htm
>
> But you cannot prove, the above model is counter model:

Again, the only "model" we are concerned here is:

n={0, 1, 2, 3, ...}
Even={0, 2, 4, 6, ... }
Odd={1, 3, 5, 7, ... }

Deal with it, Jan Burse. Quit embarrassing yourself like this.

Mostowski Collapse

unread,
May 29, 2022, 6:11:34 PM5/29/22
to
You cannot force logic to consider only one model,
if your axioms don't says so. Otherwise if the only model where:

Even={0, 2, 4, 6, ... }
Odd={1, 3, 5, 7, ... }

You could prove:

ALL(a):[a e n => [Even(a) => Even(a+2)]]
ALL(a):[a e n => [Odd(a) => Even(a+1)]]

But you cannot prove it. Because your axioms
have multiple models.

Tadd Makuda

unread,
May 29, 2022, 6:15:27 PM5/29/22
to
Mostowski Collapse wrote:

> You cannot force logic to consider only one model,
> if your axioms don't says so. Otherwise if the only model where:
> Even={0, 2, 4, 6, ... } Odd={1, 3, 5, 7, ... } You could prove:
> ALL(a):[a e n => [Even(a) => Even(a+2)]]
> ALL(a):[a e n => [Odd(a) => Even(a+1)]]
> But you cannot prove it. Because your axioms have multiple models.
> Dan Christensen schrieb am Sonntag, 29. Mai 2022 um 21:31:56 UTC+2:

<img src='data:image/
png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAwBAMAAAClLOS0AAAAElBMVEW5c17b1M3M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' alt='ae' />

Mostowski Collapse

unread,
May 29, 2022, 6:16:23 PM5/29/22
to
You are still subject to the same fallacy all over,
that Ben already pointed out. Which is getting
annoying slowly.

Lyman Uehara

unread,
May 29, 2022, 6:19:34 PM5/29/22
to

Mostowski Collapse

unread,
May 29, 2022, 6:23:44 PM5/29/22
to
Basically, using UNDEFINED to indicate an
undecided fact, we can only say that your model is:

Even(-1) = UNDEFINED
Even(0) = UNDEFINED
Even(1) = UNDEFINED
Even(2) = UNDEFINED
Etc..

because from your axioms, we even don't know
whether there is some b such that 2*b = 0 etc..

For example nothing indicates in your axioms of
EvenNextOdd that 2*0 = 0 would hold.

https://dcproof.com/EvenNextOdd.htm

LMAO!

Dan Christensen

unread,
May 29, 2022, 6:41:37 PM5/29/22
to
On Sunday, May 29, 2022 at 6:23:44 PM UTC-4, Mostowski Collapse wrote:
> Basically, using UNDEFINED to indicate an
> undecided fact, we can only say that your model is:
>
> Even(-1) = UNDEFINED
> Even(0) = UNDEFINED
> Even(1) = UNDEFINED
> Even(2) = UNDEFINED
> Etc..
>

Wrong again, Jan Burse.

Even(0) = True
Even (1) = False
Even(2) = True
Even(3) = False
etc.

Well you got one of them right. More than I expected.

> because from your axioms, we even don't know
> whether there is some b such that 2*b = 0 etc..
>

The theorems on lines 1-14 are all derivable from Peano's Axioms. They are just basic results from arithmetic on N. Deal with it, Jan Burse.

https://dcproof.com/EvenNextOdd.htm

Just admit you were wrong and quit embarrassing yourself like this, Jan Burse.

Mostowski Collapse

unread,
May 29, 2022, 6:46:24 PM5/29/22
to
Thats not what your axioms prove:

You cannot prove:

Even(0)
~Even(1)
Even(2)
~Even(3)
Etc..

From this nonsense here:
https://dcproof.com/EvenNextOdd.htm

Dan Christensen

unread,
May 29, 2022, 6:55:41 PM5/29/22
to
On Sunday, May 29, 2022 at 6:46:24 PM UTC-4, Mostowski Collapse wrote:
> Thats not what your axioms prove:
>
> You cannot prove:
>
> Even(0)
> ~Even(1)
> Even(2)
> ~Even(3)
> Etc..
>

They may well require theorems in addition to those listed on lines 1-14, e.g. that 2*0=0. So what? Get a life, Jan Burse.

https://dcproof.com/EvenNextOdd.htm

Mostowski Collapse

unread,
May 29, 2022, 7:30:09 PM5/29/22
to

Well it only shows the misery of your nonsense.
What do we know about your Even? Nothing.

The minimal requirement would be that for
a Peano numeral n* = s^n(0), we should be able

to have the following provable:

Even(n*) for n is even
~Even(n*) for n is not even
Message has been deleted

Dan Christensen

unread,
May 29, 2022, 11:57:49 PM5/29/22
to
On Sunday, May 29, 2022 at 7:30:09 PM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Montag, 30. Mai 2022 um 00:55:41 UTC+2:
> > On Sunday, May 29, 2022 at 6:46:24 PM UTC-4, Mostowski Collapse wrote:
> > > Thats not what your axioms prove:
> > >
> > > You cannot prove:
> > >
> > > Even(0)
> > > ~Even(1)
> > > Even(2)
> > > ~Even(3)
> > > Etc..
> > >
> > They may well require theorems in addition to those listed on lines 1-14, e.g. that 2*0=0. So what? Get a life, Jan Burse.
> >
> > https://dcproof.com/EvenNextOdd.htm

> What do we know about your Even?
>

See for yourself. From various theorems listed there (lines 1-14), each being derivable from Peano's Axiom, we can obtain:

(1) ALL(a):[a e n => [Even(a) => Odd(a+1)]]

(2) ALL(a):[a e n => Even(2*a) & Odd(2*a+1)]

where n = the usual set of natural numbers.

https://dcproof.com/EvenNextOdd.htm

Deal with it, Jan Burse. Do you really want to end up like JG, WM or AP?

Mostowski Collapse

unread,
May 30, 2022, 4:02:17 AM5/30/22
to
Your theorms don't make any sense. Multiplication is undefined.

The minimal requirement would be that for
a Peano numeral n* = s^n(0), we should be able

to have the following provable:

Even(n*) for n is even
~Even(n*) for n is not even

Mostowski Collapse

unread,
May 30, 2022, 5:31:20 AM5/30/22
to
Your proof would be legit, if you had:

1) A proof of:
7 ALL(a):ALL(b):[a e n & b e n => a+b=b+a]
Axiom

2) A definition of multiplication

3) A proof of:
13 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n & ~a=0 => [a*b<a*c => b<c]]
Axiom

4) A proof of:
14 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => [c<b => a*(b-c)=a*b-a*c]]
Axiom

5) A proof of:
9 ~EXIST(a):[a e n & 2*a=1]
Axiom

LMAO!

Dan Christensen

unread,
May 30, 2022, 10:00:01 AM5/30/22
to
On Monday, May 30, 2022 at 5:31:20 AM UTC-4, Mostowski Collapse wrote:
> Your proof would be legit, if you had:
>
> 1) A proof of:
> 7 ALL(a):ALL(b):[a e n & b e n => a+b=b+a]
> Axiom
>
> 2) A definition of multiplication
>
> 3) A proof of:
> 13 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n & ~a=0 => [a*b<a*c => b<c]]
> Axiom
>
> 4) A proof of:
> 14 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => [c<b => a*(b-c)=a*b-a*c]]
> Axiom
>
> 5) A proof of:
> 9 ~EXIST(a):[a e n & 2*a=1]
> Axiom
>

For readability, I usually do not list axioms/definitions/theorems that are not cited in a given proof.

Again, the purpose of the proof in question was simply to demonstrate how to use definitions of predicates: Even and and Odd being the simplest, least controversial examples. https://dcproof.com/EvenNextOdd.htm

Mostowski Collapse

unread,
May 30, 2022, 10:09:42 AM5/30/22
to
I think its quite controversial having Even with:

Even(-1) = UNDEFINED
Even(0) = UNDEFINED
Even(1) = UNDEFINED
Even(2) = UNDEFINED
Etc..

Thats not a correct definition of Even.

Mostowski Collapse

unread,
May 30, 2022, 11:07:27 AM5/30/22
to
Anyway I guess Dan Christensen has perfected the art of
dark elements. Whereby one would usually expect the following
for even natural numbers, including zero:

Even(-2) = FALSE
Even(-1) = FALSE
Even(0) = TRUE
Even(1) = FALSE
Even(2) = TRUE
Even(3) = FALSE
etc...

We seen in Dan Christensens EvenNextOdd an abundance of
dark elements. He is a real master of dark elements:

Even(-2) = UNDEFINED
Even(-1) = UNDEFINED
Even(0) = UNDEFINED
Even(1) = UNDEFINED
Even(2) = UNDEFINED
Even(3) = UNDEFINED
etc...

Dan Christensen

unread,
May 30, 2022, 11:17:17 AM5/30/22
to
On Monday, May 30, 2022 at 10:09:42 AM UTC-4, Mostowski Collapse wrote:
> I think its quite controversial having Even with:
> Even(-1) = UNDEFINED
> Even(0) = UNDEFINED
> Even(1) = UNDEFINED
> Even(2) = UNDEFINED
> Etc..


Liar. Again, using nothing more than basic arithmetic (e.g . 2*0=0 and 2*1=2) we can obtain from my proof:

Even(0) = True
Even(1) = False
Even(2) = True
etc.

Aren't you getting tired of looking like an complete idiot, Jan Burse? I am getting bored with your silly games.

Dan
0 new messages