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.

STUDENTS BEWARE: Don't be a victim of JG's fake math

On Wednesday, April 13, 2022 at 2:57:45 AM UTC-4, I am Super Rectum (aka John Gabriel (JG), Troll Boy) wrote:
> First learn how ...

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

STUDENTS BEWARE: Dan Christensen is the troll
who presents us with function spaces that have one element.

Dan Christensen schrieb am Mittwoch, 13. April 2022 um 14:39:14 UTC+2:
> STUDENTS BEWARE: Don't be a victim of JG's fake math

On Wednesday, April 13, 2022 at 8:53:44 AM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> STUDENTS BEWARE: Dan Christensen is the troll
> who presents us with function spaces that have one element.
> Dan Christensen schrieb am Mittwoch, 13. April 2022 um 14:39:14 UTC+2:
> > STUDENTS BEWARE: Don't be a victim of JG's fake math

Sooooo cute the way you "stick up" for your little buddy here. (A match made in heaven!)

You can learn a lot from Jan Burse. Listen very carefully to him. And do the opposite to what he says. I have found him very useful in this regard. He, for example, wants to promote his theory of "dark elements" -- making inferences about functions outside of their domains of definitions (Burse's Paradox). It recently inspired me to sharpen my notion of a function. Well done, Jan! (Hee, hee!)

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 was thinking very hard :
> STUDENTS BEWARE: Dan Christensen is the troll
> who presents us with function spaces that have one element.

ISTR an entire structure with a one element set and two functions - one
a partial function.

You can define two different equalities:

=_1 : Via Dan Christensens ad-hoc Axiom 1
For =_1 we can prove:
ALL(f):ALL(g):[f = g]

=_2 : Try this axiom ALL(f):ALL(g):[EXIST(a):[~f(a)=g(a)] => ~f=g]
For =_2 we cannot prove:
ALL(f):ALL(g):[f = g]

But neither captures Terrence Tao, Terrence Tao is more difficult.
=_2 only captures equality of first order function symbols.

FromTheRafters schrieb am Mittwoch, 13. April 2022 um 17:00:54 UTC+2:
> Mostowski Collapse was thinking very hard :
> > STUDENTS BEWARE: Dan Christensen is the troll
> > who presents us with function spaces that have one element.
> ISTR an entire structure with a one element set and two functions - one
> a partial function.

The =_2 axiom is basically a form of:
indiscernibility of identicals
https://en.wikipedia.org/wiki/Identity_of_indiscernibles

Take contraposition of the axiom
ALL(f):ALL(g):[EXIST(a):[~f(a)=g(a)] => ~f=g]
and you get:
ALL(f):ALL(g):[f=g => ALL(a):[f(a)=g(a)]]

Now you can use for F=(a,b) that F(h) :<=> h(a)=b and you get:
ALL(f):ALL(g):[f=g => ALL(F):[F(f) <=> F(g)]]
Or set theoretically F(h) :<=> (a,b) e h and you get:
ALL(f):ALL(g):[f=g => ALL(a):ALL(b):[(a,b) e f <=> (a,b) e g]]

Which you get for free in ZFC, since it is based on FOL with equality.
The other direction "identity of indiscernibles" has also some
challenges, which one might need to master. We might be tempted

to derive via extensionality in ZFC that:
ALL(f):ALL(g):[ALL(a):ALL(b):[(a,b) e f <=> (a,b) e g] => f=g]

But this would be fallacious, even ZFC extensionality does
not say exactly this, since a set need not only have pairs as it
members. So you might need something more

complicated. Gödel did such things in his booklet.

Mostowski Collapse schrieb am Mittwoch, 13. April 2022 um 19:42:47 UTC+2:
> You can define two different equalities:
>
> =_1 : Via Dan Christensens ad-hoc Axiom 1
> For =_1 we can prove:
> ALL(f):ALL(g):[f = g]
>
> =_2 : Try this axiom ALL(f):ALL(g):[EXIST(a):[~f(a)=g(a)] => ~f=g]
> For =_2 we cannot prove:
> ALL(f):ALL(g):[f = g]
>
> But neither captures Terrence Tao, Terrence Tao is more difficult.
> =_2 only captures equality of first order function symbols.
> FromTheRafters schrieb am Mittwoch, 13. April 2022 um 17:00:54 UTC+2:
> > Mostowski Collapse was thinking very hard :
> > > STUDENTS BEWARE: Dan Christensen is the troll
> > > who presents us with function spaces that have one element.
> > ISTR an entire structure with a one element set and two functions - one
> > a partial function.

It happens that Mostowski Collapse formulated :
> You can define two different equalities:
>
> =_1 : Via Dan Christensens ad-hoc Axiom 1
> For =_1 we can prove:
> ALL(f):ALL(g):[f = g]
>
> =_2 : Try this axiom ALL(f):ALL(g):[EXIST(a):[~f(a)=g(a)] => ~f=g]
> For =_2 we cannot prove:
> ALL(f):ALL(g):[f = g]
>
> But neither captures Terrence Tao, Terrence Tao is more difficult.
> =_2 only captures equality of first order function symbols.
>
> FromTheRafters schrieb am Mittwoch, 13. April 2022 um 17:00:54 UTC+2:
>> Mostowski Collapse was thinking very hard :
>>> STUDENTS BEWARE: Dan Christensen is the troll
>>> who presents us with function spaces that have one element.
>> ISTR an entire structure with a one element set and two functions - one
>> a partial function.

I wanted a new car with no sunroof. Didn't want a sunroof? actually
wanted to 'not have' a sunroof. The dealer somehow didn't see the
difference between my 'not wanting' to spring for a sunroof financially
and my actual wanting to not have a sunroof.

Sometimes it is hard to see what a particular statement doesn't say,
and perhaps should, rather than what it does say.

How it started:
Russia: We have captured a highly advanced radar
and coms station previously never seen before
How its going:
Ukraine: Its a lamp

How it started:
Dan: DC Proof is for text book mathematics
How its going:
One defective axiom after the other

To put this in relation:
Dan chews already for years on a single page of
Terrence Tao where Tao introduces functions,
whereas Taos text book has surely 400 pags or so.

FromTheRafters schrieb am Mittwoch, 13. April 2022 um 21:47:29 UTC+2:
> It happens that Mostowski Collapse formulated :
> > You can define two different equalities:
> >
> > =_1 : Via Dan Christensens ad-hoc Axiom 1
> > For =_1 we can prove:
> > ALL(f):ALL(g):[f = g]
> >
> > =_2 : Try this axiom ALL(f):ALL(g):[EXIST(a):[~f(a)=g(a)] => ~f=g]
> > For =_2 we cannot prove:
> > ALL(f):ALL(g):[f = g]
> >
> > But neither captures Terrence Tao, Terrence Tao is more difficult.
> > =_2 only captures equality of first order function symbols.
> >
> > FromTheRafters schrieb am Mittwoch, 13. April 2022 um 17:00:54 UTC+2:
> >> Mostowski Collapse was thinking very hard :
> >>> STUDENTS BEWARE: Dan Christensen is the troll
> >>> who presents us with function spaces that have one element.
> >> ISTR an entire structure with a one element set and two functions - one
> >> a partial function.
> I wanted a new car with no sunroof. Didn't want a sunroof? actually
> wanted to 'not have' a sunroof. The dealer somehow didn't see the
> difference between my 'not wanting' to spring for a sunroof financially
> and my actual wanting to not have a sunroof.
>
> Sometimes it is hard to see what a particular statement doesn't say,
> and perhaps should, rather than what it does say.

Anyway big respect for those that developed Coq,
Isabelle/HOL, etc.. and those that use these tools to
formalize tons of mathematics....

Mostowski Collapse schrieb am Donnerstag, 14. April 2022 um 00:10:24 UTC+2:
> How it started:
> Russia: We have captured a highly advanced radar
> and coms station previously never seen before
> How its going:
> Ukraine: Its a lamp
>
> How it started:
> Dan: DC Proof is for text book mathematics
> How its going:
> One defective axiom after the other
>
> To put this in relation:
> Dan chews already for years on a single page of
> Terrence Tao where Tao introduces functions,
> whereas Taos text book has surely 400 pags or so.
> FromTheRafters schrieb am Mittwoch, 13. April 2022 um 21:47:29 UTC+2:
> > It happens that Mostowski Collapse formulated :
> > > You can define two different equalities:
> > >
> > > =_1 : Via Dan Christensens ad-hoc Axiom 1
> > > For =_1 we can prove:
> > > ALL(f):ALL(g):[f = g]
> > >
> > > =_2 : Try this axiom ALL(f):ALL(g):[EXIST(a):[~f(a)=g(a)] => ~f=g]
> > > For =_2 we cannot prove:
> > > ALL(f):ALL(g):[f = g]
> > >
> > > But neither captures Terrence Tao, Terrence Tao is more difficult.
> > > =_2 only captures equality of first order function symbols.
> > >
> > > FromTheRafters schrieb am Mittwoch, 13. April 2022 um 17:00:54 UTC+2:
> > >> Mostowski Collapse was thinking very hard :
> > >>> STUDENTS BEWARE: Dan Christensen is the troll
> > >>> who presents us with function spaces that have one element.
> > >> ISTR an entire structure with a one element set and two functions - one
> > >> a partial function.
> > I wanted a new car with no sunroof. Didn't want a sunroof? actually
> > wanted to 'not have' a sunroof. The dealer somehow didn't see the
> > difference between my 'not wanting' to spring for a sunroof financially
> > and my actual wanting to not have a sunroof.
> >
> > Sometimes it is hard to see what a particular statement doesn't say,
> > and perhaps should, rather than what it does say.