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tech / sci.math / Re: Dan Christensen is Bat Shit Crazy

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* 16 May 2022: New visitors to sci.math: The New Calculus is the firstEram semper recta
`* STUDENTS BEWARE: Don't be a victim of John Gabriel's fake mathDan Christensen
 `* Dan Christensen is Bat Shit CrazyMostowski Collapse
  `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   +* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
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   |`* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   | `* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |  +* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |  |`- Re: Dan Christensen is Bat Shit CrazyBill Monti Hida
   |  `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |   `* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |    +- Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |    `* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |     `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |      `* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
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   |       `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |        `* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |         `* Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |          `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |           `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |            +- Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |            +- Re: Dan Christensen is Bat Shit CrazyMostowski Collapse
   |            `* Re: Dan Christensen is Bat Shit CrazyDan Christensen
   |             `- Re: Dan Christensen is Bat Shit CrazyAi Abe
   `- Re: Dan Christensen is Bat Shit CrazyJan Baisotei

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

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Subject: 16 May 2022: New visitors to sci.math: The New Calculus is the first
rigorous formulation in history.
From: thenewca...@gmail.com (Eram semper recta)
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 by: Eram semper recta - Mon, 16 May 2022 04:54 UTC

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.


Click here to read the complete article
STUDENTS BEWARE: Don't be a victim of John Gabriel's fake math

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Subject: STUDENTS BEWARE: Don't be a victim of John Gabriel's fake math
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Mon, 16 May 2022 05:10 UTC

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

Dan Christensen is Bat Shit Crazy

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From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 19:09 UTC

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!

Re: Dan Christensen is Bat Shit Crazy

<70b3c69b-f4b2-4f85-b4ad-69f8747cf2b0n@googlegroups.com>

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Mon, 16 May 2022 20:30 UTC

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 21:56 UTC

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.

Dan Christensen schrieb am Montag, 16. Mai 2022 um 22:30:37 UTC+2:
> 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 22:00 UTC

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)]]

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)]]
>
> 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.
> Dan Christensen schrieb am Montag, 16. Mai 2022 um 22:30:37 UTC+2:
> > 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

Re: Dan Christensen is Bat Shit Crazy

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From: bno...@taoatbst.sa (Jan Baisotei)
Newsgroups: sci.math
Subject: Re: Dan Christensen is Bat Shit Crazy
Date: Mon, 16 May 2022 22:48:45 -0000 (UTC)
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 by: Jan Baisotei - Mon, 16 May 2022 22:48 UTC

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.

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Tue, 17 May 2022 02:26 UTC

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
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 by: Mostowski Collapse - Tue, 17 May 2022 06:56 UTC

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

Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 04:26:54 UTC+2:
> 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

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 by: Mostowski Collapse - Tue, 17 May 2022 09:54 UTC

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

Mostowski Collapse schrieb am Dienstag, 17. Mai 2022 um 08:56:28 UTC+2:
> 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
> Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 04:26:54 UTC+2:
> > 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
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 by: Bill Monti Hida - Tue, 17 May 2022 10:11 UTC

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/

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Tue, 17 May 2022 13:40 UTC

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Tue, 17 May 2022 14:05 UTC

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 schrieb am Dienstag, 17. Mai 2022 um 15:40:50 UTC+2:
> 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Tue, 17 May 2022 14:32 UTC

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

Dan

On Tuesday, May 17, 2022 at 10:05:28 AM UTC-4, Mostowski Collapse wrote:
> 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 schrieb am Dienstag, 17. Mai 2022 um 15:40:50 UTC+2:
> > 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Tue, 17 May 2022 14:34 UTC

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.

Mostowski Collapse schrieb am Dienstag, 17. Mai 2022 um 16:05:28 UTC+2:
> 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 schrieb am Dienstag, 17. Mai 2022 um 15:40:50 UTC+2:
> > 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Tue, 17 May 2022 14:42 UTC

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
Injection-Date: Tue, 17 May 2022 14:54:07 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Mostowski Collapse - Tue, 17 May 2022 14:54 UTC

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

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!!!
>
> Dan

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
Injection-Date: Tue, 17 May 2022 14:58:47 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Mostowski Collapse - Tue, 17 May 2022 14:58 UTC

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).

Mostowski Collapse schrieb am Dienstag, 17. Mai 2022 um 16:54:14 UTC+2:
> 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
> 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!!!
> >
> > Dan

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
Injection-Date: Tue, 17 May 2022 15:09:42 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Dan Christensen - Tue, 17 May 2022 15:09 UTC

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
Injection-Date: Tue, 17 May 2022 15:13:09 +0000
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 by: Mostowski Collapse - Tue, 17 May 2022 15:13 UTC

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?

Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 17:09:49 UTC+2:
> 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Tue, 17 May 2022 15:17 UTC

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)]]

Mostowski Collapse schrieb am Dienstag, 17. Mai 2022 um 17:13:14 UTC+2:
> 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?
> Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 17:09:49 UTC+2:
> > 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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
Injection-Date: Tue, 17 May 2022 19:38:25 +0000
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 by: Dan Christensen - Tue, 17 May 2022 19:38 UTC

On Tuesday, May 17, 2022 at 11:17:11 AM UTC-4, Mostowski Collapse wrote:

> Mostowski Collapse schrieb am Dienstag, 17. Mai 2022 um 17:13:14 UTC+2:
> > 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?
> > Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 17:09:49 UTC+2:
> > > 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.

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

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: Dan_Chri...@sympatico.ca (Dan Christensen)
Injection-Date: Tue, 17 May 2022 19:47:33 +0000
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 by: Dan Christensen - Tue, 17 May 2022 19:47 UTC

On Tuesday, May 17, 2022 at 3:38:30 PM UTC-4, Dan Christensen wrote:
> On Tuesday, May 17, 2022 at 11:17:11 AM UTC-4, Mostowski Collapse wrote:
>
> > Mostowski Collapse schrieb am Dienstag, 17. Mai 2022 um 17:13:14 UTC+2:
> > > 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?
> > > Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 17:09:49 UTC+2:
> > > > 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.
> 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))]]

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.

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

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 18 May 2022 00:08 UTC

You cannot prove this from your Axioms:

~EXIST(a):[a < 0]

What would be the proof?

Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 21:47:38 UTC+2:
> ~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.

Re: Dan Christensen is Bat Shit Crazy

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Subject: Re: Dan Christensen is Bat Shit Crazy
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 18 May 2022 00:11 UTC

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?

Mostowski Collapse schrieb am Mittwoch, 18. Mai 2022 um 02:08:29 UTC+2:
> You cannot prove this from your Axioms:
>
> ~EXIST(a):[a < 0]
>
> What would be the proof?
> Dan Christensen schrieb am Dienstag, 17. Mai 2022 um 21:47:38 UTC+2:
> > ~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.

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