16 May 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.

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]

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

On Monday, May 16, 2022 at 12:54:21 AM UTC-4, I am Super Rectum (aka John Gabriel (JG), Troll Boy) wrote:

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

[Mostowski Collapse]

STUDENTS BEWARE: Don't be a victim of Dan Christensens fake math
He tries to sell us some even and odd natural numbers, but he cannot prove:

~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]

Dan Christensen schrieb am Montag, 16. Mai 2022 um 07:10:09 UTC+2:
> Dan Christensens Pathetic Daily Spam Post -- Same AGAIN and AGAIN!

[Dan Christensen]

On Monday, May 16, 2022 at 3:09:44 PM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> STUDENTS BEWARE: Don't be a victim of Dan Christensens fake math
> He tries to sell us some even and odd natural numbers, but he cannot prove:
>
> ~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]
>

Easy. 0 is an even number and no natural number is less than 0. You didn't know that, Jan Burse? Sorry, your "dark elements" don't count.

Poor Jan Burse still 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

[Mostowski Collapse]

This formula is also not provable from your axioms here:
https://dcproof.com/EvenNextOdd.htm

~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]

On the same reason that your axioms are also satisfied
by Z, the set of positive and negative integers.

There is not a single axiom that would prevent interpreting
<n=N, +> as <n=Z, +> in your axioms. The other signs - and < are
anyway derived. Because of these many possible

interpretations, the above formula cannot be proved,
although it holds for the even natural numbers, but
it does not hold for the even positive and negative integers,

and since <n=Z, +> satisfies your axioms, the logic
will not decide in favor of one of the models, and leave
the formula unprovable. You can also view <n=Z, +>

as a counter model to the above formula.

[Mostowski Collapse]

Corr.: The unprovable formula, that is satisfied in N, is this here,
there was a slight typo in the second Even predicate occurence:

~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]

[Jan Baisotei]

Dan Christensen wrote:

>> ~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]
>
> Easy. 0 is an even number and no natural number is less than 0. You
> didn't know that, Jan Burse? Sorry, your "dark elements" don't count.

Hi, nice to meet you. Io sono communisto, how are you? Proud of me being
io sono communisto.

[Dan Christensen]

On Monday, May 16, 2022 at 5:56:13 PM UTC-4, Mostowski Collapse wrote:
> This formula is also not provable from your axioms here:
> https://dcproof.com/EvenNextOdd.htm
>
> ~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]
>

Even if true, it would be irrelevant. Again, the axioms listed at the beginning of my proof are just some results from basic arithmetic that were required for this proof about even and odd numbers. In a formal proof, you must make every one of your assumptions explicit. If you want to use the fact that the natural numbers are closed under addition, you must state that in your initial assumptions (line 6 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]

The axioms are not specific to N. Could be anything. Not
a very useful example. Your Even is not even natural numbers.
Means its a definition of the even natural numbers.

Even F_4 satisfies your axioms? F_4 has the following addition
and multiplication table:

+ 0 1 2 3
0 0 1 2 3
1 1 2 3 0
2 2 3 0 1
3 3 0 1 2

* 0 1 2 3
0 0 0 0 0
1 0 1 2 3
2 0 2 0 2
3 0 3 2 1

[Mostowski Collapse]

You can use Prolog to verify this axiom:

14 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n & ~a=0 => [a*b<a*c => b<c]]
Axiom

This query tells that it works in F_4:

?- domain(A), A \== 0, domain(B), domain(C), times(A,B,X), times(A,C,Y), less(X,Y), \+ less(B,C).
false.

---------------------------- begin prolog code ----------------------------------------

/***********************************************************/
/* F4 */
/***********************************************************/

domain(0).
domain(1).
domain(2).
domain(3).

plus(A, B, C) :- C is (A+B) mod 4.

times(A, B, C) :- C is (A*B) mod 4.

/***********************************************************/
/* Dan */
/***********************************************************/

% 13 ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 & a+c=b]]]
% Axiom
less(A, B) :- domain(C), C \== 0, plus(A, C, B).

---------------------------- end prolog code ----------------------------------------

[Bill Monti Hida]

Mostowski Collapse wrote:

> You can use Prolog to verify this axiom:

> ---------------------------- begin prolog code

> /***********************************************************/
> /* F4 */
> /***********************************************************/
> domain(0).
> domain(1).

> /***********************************************************/
> /* Dan */
> /***********************************************************/
> % 13 ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 &

nothing. Bye.

Americans fly to Ukraine to fight against the Ukrainian Nazi Azov and
liberalism https://www.bitchute.com/video/XTVdnlhieOl2/

Zelensky has accused the Russian Army of shelling schools and
kindergartens https://www.bitchute.com/video/j8vgi9iNo8uc/

[Dan Christensen]

On Tuesday, May 17, 2022 at 2:56:28 AM UTC-4, Mostowski Collapse wrote:
> The axioms are not specific to N.

Irrelevant. They are among the properties of +, -, * and < on N. Deal with it, Jan Burse.

Dan

[Mostowski Collapse]

You originally wrote the following, in your Case 1 and Case 2 thread:
(In both cases, n = the set of natural numbers.)

But its a lie, the n of your EvenNextOdd.htm can be anything.
You also use axioms that fell from the sky like for example:

10 ~EXIST(a):[a e n & 2*a=1]
Axiom
https://dcproof.com/EvenNextOdd.htm

Where do you prove that from Peano.
Also you are subject to the following fallacy:

Commutation of Conditionals Fallacy
(A => B) => (B => A)

You think if you use Axioms where one can see Peano
=> Axiom, that this would also say Axiom => Peano.

[Dan Christensen]

See my reply just now to your nearly identical posting at sci.logic.

Dan

[Mostowski Collapse]

You Commutation of Conditionals Fallacy is seen here, when you wrote:

> ~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]
> Easy. 0 is an even number and no natural number is less than 0.

What the heck? Appeal to intended model? LoL
Try this here model here, does it satisfy the above formula?

+ 0 1 2 3
0 0 1 2 3
1 1 2 3 0
2 2 3 0 1
3 3 0 1 2

* 0 1 2 3
0 0 0 0 0
1 0 1 2 3
2 0 2 0 2
3 0 3 2 1

I didn't check yet. But your < is quite currious in such a model.

[Dan Christensen]

On Tuesday, May 17, 2022 at 10:34:17 AM UTC-4, Mostowski Collapse wrote:
> You Commutation of Conditionals Fallacy is seen here, when you wrote:
>
> > ~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]
> > Easy. 0 is an even number and no natural number is less than 0.
> What the heck? Appeal to intended model? LoL
> Try this here model here, does it satisfy the above formula?
> + 0 1 2 3
> 0 0 1 2 3
> 1 1 2 3 0
> 2 2 3 0 1
> 3 3 0 1 2
>
> * 0 1 2 3
> 0 0 0 0 0
> 1 0 1 2 3
> 2 0 2 0 2
> 3 0 3 2 1

Are you really claiming that there exists a natural number less than 0??? One of those "dark elements" of yours, Jan Burse? HA, HA, HA!!!

Dan

[Mostowski Collapse]

You can try yourself. Your theory here, especially what
you call common rules of basic arithmetic (line 1-14):
https://dcproof.com/EvenNextOdd.htm

Is satisfied by F4:

+ 0 1 2 3
0 0 1 2 3
1 1 2 3 0
2 2 3 0 1
3 3 0 1 2

* 0 1 2 3
0 0 0 0 0
1 0 1 2 3
2 0 2 0 2
3 0 3 2 1

[Mostowski Collapse]

Your definition of (<)/2, is this here:
% 13 ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 & a+c=b]]]
% Axiom

Its only a valid definition of a < b for the natural numbers.
But if the model is not the natural numbers, it is nonsense.

You can check yourself:

?- domain(A), domain(B), write(A), write(', '), write(B), write(': '),
| (less(A,B) -> write(yes); write(no)), nl, fail; true.
0, 0: no
0, 1: yes
0, 2: yes
0, 3: yes
1, 0: yes
1, 1: no
1, 2: yes
1, 3: yes
2, 0: yes
2, 1: yes
2, 2: no
2, 3: yes
3, 0: yes
3, 1: yes
3, 2: yes
3, 3: no
true.

The Prolog code to explore your definition is relatively simple:

domain(0).
domain(1).
domain(2).
domain(3).

plus(A, B, C) :- C is (A+B) mod 4.

less(A, B) :- domain(C), C \== 0, plus(A, C, B).

[Dan Christensen]

On Tuesday, May 17, 2022 at 10:54:14 AM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 16:42:58 UTC+2:
> > On Tuesday, May 17, 2022 at 10:34:17 AM UTC-4, Mostowski Collapse wrote:
> > > You Commutation of Conditionals Fallacy is seen here, when you wrote:
> > >
> > > > ~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]
> > > > Easy. 0 is an even number and no natural number is less than 0.
> > > What the heck? Appeal to intended model? LoL
> > > Try this here model here, does it satisfy the above formula?
> > > + 0 1 2 3
> > > 0 0 1 2 3
> > > 1 1 2 3 0
> > > 2 2 3 0 1
> > > 3 3 0 1 2
> > >
> > > * 0 1 2 3
> > > 0 0 0 0 0
> > > 1 0 1 2 3
> > > 2 0 2 0 2
> > > 3 0 3 2 1
> > Are you really claiming that there exists a natural number less than 0??? One of those "dark elements" of yours, Jan Burse? HA, HA, HA!!!

Please answer the question, Jan Burse.

Dan

[Mostowski Collapse]

I am still claiming the same as before:

Mostowski Collapse schrieb am Montag, 16. Mai 2022 um 23:56:13 UTC+2:
> This formula is also not provable from your axioms here:
> https://dcproof.com/EvenNextOdd.htm
>

> ~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]
https://groups.google.com/g/sci.math/c/B_nrhs-QQ7w/m/ZmC-DZqkBwAJ

Why do you ask?

[Mostowski Collapse]

In F4 its very easy to see. Since your < degenerates to a =\= b.
So if you have at least two evens, like Even(0) and Even(2),

this formula cannot be satisfied:

~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]

[Dan Christensen]

Still no answer? Oh, well....

> In F4 its very easy to see. Since your < degenerates to a =\= b.
> So if you have at least two evens, like Even(0) and Even(2),
>
> this formula cannot be satisfied:
> ~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]

Huh??? We were talking about:

~ALL(a):[a e n => (Even(a) => EXIST(b):[b e n & b < a & Odd(b))]]

[Dan Christensen]

You later changed to:

~ALL(a):[a e n & Even(a) => EXIST(b):[b e n & b < a & Even(b)]]

The analysis is still the same. The counter-example in both cases is a=0: There is no natural number < 0.

[Mostowski Collapse]

You cannot prove this from your Axioms:

~EXIST(a):[a < 0]

What would be the proof?

[Mostowski Collapse]

Or more precisely, you cannot prove this:

~EXIST(a):[a e n & a < 0]

From your axioms here:

common rules of basic arithmetic (line 1-14)
https://dcproof.com/EvenNextOdd.htm

What should be the proof?

[Dan Christensen]

On Tuesday, May 17, 2022 at 8:11:53 PM UTC-4, Mostowski Collapse wrote:
> Or more precisely, you cannot prove this:
>
> ~EXIST(a):[a e n & a < 0]
>

Again, even if true, it would be irrelevant. Not even you can deny that the results from basic arithmetic on N that I list in lines 1-14 and the definition of Even and Odd on N on lines 15-16 are sufficient to prove:

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

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

Where n is the set of natural numbers.

https://dcproof.com/EvenNextOdd.htm

Just admit your were wrong, Jan Burse. You are looking very crankish indeed. Your little buddy and fellow troll JG here must really be getting to you. (Wink-wink!)

Dan

[Ai Abe]

Dan Christensen wrote:

> On Tuesday, May 17, 2022 at 8:11:53 PM UTC-4, Mostowski Collapse wrote:
>> Or more precisely, you cannot prove this: ~EXIST(a):[a e n & a < 0]
>
> Again, even if true, it would be irrelevant. Not even you can deny that
> the results from basic arithmetic on N that I list in lines 1-14 and the
> definition of Even and Odd on N on lines 15-16 are sufficient to prove:

European Parliament Plans to Add Former German Chancellor Schroeder to Sanctions List: Report
https://sputniknews.com/20220518/european-parliament-plans-to-add-former-german-chancellor-schroder-to-sanctions-list-1095602542.html