The incorrigible morons of mainstream academia define an "irrational number" as:

"An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html

And then this:

The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.

In other words π = C : 2r

However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.

By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.

Learn what is a number in mathematics exactly:

https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq

Students:

The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.

Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.

At the Mathworld link(https://mathworld.wolfram.com/Ratio.html#:~:text=The%20ratio%20of%20two%20numbers,is%20equivalent%20to%20the%20quotient%20.), the ratio is defined to be a *fraction* of two numbers (numerator and denominator), but neither circumference nor diameter are necessarily ***numbers***.

See what I mean by paying attention to detail my dear students? :)

Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed.

On Thursday, 1 July 2021 at 10:39:14 UTC-4, Eram semper recta wrote:
> The incorrigible morons of mainstream academia define an "irrational number" as:
>
> "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
>
> And then this:
>
> The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
>
> In other words π = C : 2r
>
> However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
>
> By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
>
> Learn what is a number in mathematics exactly:
>
> https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
>
> Students:
>
> The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
>
> Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
>
> At the Mathworld link(https://mathworld.wolfram.com/Ratio.html#:~:text=The%20ratio%20of%20two%20numbers,is%20equivalent%20to%20the%20quotient%20.), the ratio is defined to be a *fraction* of two numbers (numerator and denominator), but neither circumference nor diameter are necessarily ***numbers***.
>
> See what I mean by paying attention to detail my dear students? :)
>
> Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed.

So in one link, the baboons who run Mathworld say an "irrational number" cannot be written as a *fraction* and in another link, they say that pi can be written as a fraction of two numbers. Which is it? :)

Tsk, tsk.

On Thursday, July 1, 2021 at 3:41:20 PM UTC+1, Eram semper recta wrote:

"Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed. So in one link, the baboons who run Mathworld say an "irrational number" cannot be written as a *fraction* and in another link, they say that pi can be written as a fraction of two numbers. Which is it? :) . Tsk, tsk."

Common sense might suggest that in one case they were being more formal in thinking of a pair of integers, and in the other they were speaking more informally. As would be obvious to just about anyone. Perhaps they respect the intellectual capacity of their audience (outliers like yourself aren't worth taking into account). I was using that website when I was a first year undergraduate and never had any problems with it. By contrast you have nothing meaningful to say, so your ego needs to invent a fault where none of substance exists. Tut tut tut...

If your ability to read mathematics is that poor, why would any student want to waste their time with your 160+ page tome full of rookie errors and poor quality presentation?

Oh, and when are we going to see either:

1) a derivation of the Euler-Lagrange Equation in the new calculus without using limits by stealth (he, he, he...). Your approach is an utter waste of time if it can't handle core classical physics (let alone general relativity and quantum mechanics).

2) A solution to any of the unsolved Erdos problems using your approach (surely easy for the self-acclaimed 'greatest mathematician since Archimedes' LOL). After all, Erdos was the great number theorist of the 20th century, so if you claim to understand numbers better than he did...

3) any evidence of your laughable claims to have an IQ over 4 standard deviations above average (got the nerve to even take me on in a Mensa contest yet? thought not).

Come to think of it, do you even have a degree in mathematics?, and if so what level and from which institution?

Aside from offering comedy material to Dan Christensen, what is the point of many of these posts of yours? The actual intellectual content seems to be nil. Is the NPD bad enough that this is the only way to experience ego highs at this stage? You should take my advice and have a go at gardening. Getting our in the sun would do you some good.

Have a wonderful day.

On Thursday, 1 July 2021 at 11:06:00 UTC-4, Cowardly anonmymous moron going by Quantum Babbling aka ross.pro...@gmx.com wrote:
> On Thursday, July 1, 2021 at 3:41:20 PM UTC+1, Eram semper recta wrote:
>
> "Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed. So in one link, the baboons who run Mathworld say an "irrational number" cannot be written as a *fraction* and in another link, they say that pi can be written as a fraction of two numbers. Which is it? :) . Tsk, tsk."
>
> Common sense

You don't have any common sense, so you really shouldn't be talking about this. Chuckle.

> might suggest that in one case they were being more formal in thinking of a pair of integers, and in the other they were speaking more informally.

In mathematics, REAL mathematicians talk **formally and logically** without any inconsistencies.

Students:

As you can see, this is the appearance of a specific kind of troll who wants you to think he is civil, educated and knows mathematics. He presents a non-argument and then goes off on a tangent about another idiot mathematician called Erdos who is worshipped by the mainstream cult.

The bullshitter claims they were thinking of a pair of integers, but does not address the topic as to what "they", the baboons of mainstream academia mean when they call C/2r a fraction, for by definition, a fraction has a numerator and denominator. This fucking Limey scumbag who knows SHIT about mathematics, did not even attempt to refute this fact. One look at his numerous drivel on this site will show you that all he does is write long meaningless essays filled with irrelevant opinions and errors.

Do you want to be an idiot like this fool?

Again, this is a once off comment to warn students of fools who appear to be erudite, who claim to have many degrees, but are in reality insignificant and ignorant nobodies such as this coward who is constantly polluting my threads without revealing his real name. I shall find out who he is and I will get him kicked off sci.math even though it is unmoderated.

He will suffer the same fate as Port563 (scumbag Gilbert Strang of MIT).

Eram semper recta <thenewcalculus@gmail.com> wrote:
> On Thursday, 1 July 2021 at 11:06:00 UTC-4, Quantum Bubbles
> <ross.pro...@gmx.com> wrote:
>> On Thursday, July 1, 2021 at 3:41:20 PM UTC+1, Eram semper recta
>> wrote:

>> Common sense

> You don't have any common sense, so you really shouldn't be talking
> about this. Chuckle.

>> might suggest that in one case they were being more formal in thinking
>> of a pair of integers, and in the other they were speaking more
>> informally.

> In mathematics, REAL mathematicians talk **formally and logically**
> without any inconsistencies.

In my experience mathematicians speak with as much informality as any
other intellectual group. In informal language, there are likely to
appear superficial inconsistencies, which however vanish when formality
returns to the discussion.

> Students:

> As you can see, this is the appearance of a specific kind of troll who
> wants you to think he is civil, educated and knows mathematics. He
> presents a non-argument and then goes off on a tangent about another
> idiot mathematician called Erdos who is worshipped by the mainstream
> cult.

You're becoming more and more like Archimedes Plutonium. You're slagging
off successful people at random, pehaps out of an angry jealousy.

> The bullshitter claims they were thinking of a pair of integers, but
> does not address the topic as to what "they", the baboons of mainstream
> academia mean when they call C/2r a fraction, for by definition, a
> fraction has a numerator and denominator. This fucking Limey scumbag
> who knows SHIT about mathematics, did not even attempt to refute this
> fact. One look at his numerous drivel on this site will show you that
> all he does is write long meaningless essays filled with irrelevant
> opinions and errors.

_You_ know little about maths, John Gabriel. You don't understand
limits, you don't understand axioms, you don't understand set theory, and
you don't understand calculus. You don't have a degree in maths.
Quantum Bubles has several such degrees, and clearly knows his way around
the mathematical literature.

> Do you want to be an idiot like this fool?

> Again, this is a once off comment to warn students of fools who appear
> to be erudite, who claim to have many degrees, but are in reality
> insignificant and ignorant nobodies such as this coward who is
> constantly polluting my threads without revealing his real name.

He's just being sensible not revealing his name. He even justified it at
one point. You've threatened him with physical violence, don't forget.
Perhaps you should reveal your real name and address, if you're not a
coward yourself, so as to enable people to call law enforcement on you
should you commit further criminal offences.

> I shall find out who he is and I will get him kicked off sci.math even
> though it is unmoderated.

Why? Because he can effectively hold a mirror in front of you so that
you can see who and what you are?

> He will suffer the same fate as Port563 (scumbag Gilbert Strang of
> MIT).

As far as I can make out, Dr. Strang is doing rather well at MIT. The
only person in this discussion "suffering a fate" is you.

--
Alan Mackenzie (Nuremberg, Germany).

On Thursday, 1 July 2021 at 10:39:14 UTC-4, Eram semper recta wrote:
> The incorrigible morons of mainstream academia define an "irrational number" as:
>
> "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
>
> And then this:
>
> The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
>
> In other words π = C : 2r
>
> However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
>
> By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
>
> Learn what is a number in mathematics exactly:
>
> https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
>
> Students:
>
> The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
>
> Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
>
> At the Mathworld link(https://mathworld.wolfram.com/Ratio.html#:~:text=The%20ratio%20of%20two%20numbers,is%20equivalent%20to%20the%20quotient%20.), the ratio is defined to be a *fraction* of two numbers (numerator and denominator), but neither circumference nor diameter are necessarily ***numbers***.
>
> See what I mean by paying attention to detail my dear students? :)
>
> Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed.

Students:

Look carefully ... there has not been a single attempt to refute what I claim. Your conclusion? :)

On Thursday, July 1, 2021 at 7:39:14 AM UTC-7, Eram semper recta wrote:
> The incorrigible morons of mainstream academia define an "irrational number" as:
>
> "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
>
> And then this:
>
> The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
>
> In other words π = C : 2r
>
> However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.

It is two quantities that operationally divide. A fraction is the same division operation.
The round formula needs measurement first...

>
> By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
>
> Learn what is a number in mathematics exactly:
>
> https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
>
> Students:
>
> The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
>
> Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.

They share a sameness as a division operation of two quantities you moron....

Mitchell Raemsch.

On 7/1/2021 7:39 AM, Eram semper recta wrote:
> The incorrigible morons of mainstream academia define an "irrational number" as a number that is not rational

Shut up idiot.

On Friday, July 2, 2021 at 1:47:16 AM UTC+1, Eram semper recta wrote:

"Look carefully ... there has not been a single attempt to refute what I claim."

In one comment you make a false insinuation concerning logical correctness. The falsity of this insinuation has been adequately highlighted by myself and the ever sensible Alan Mackenzie . Therefore one of your claims has been rebutted here. English comprehension seems to be a special difficulty for you. If English is not your first language that is perhaps understandable, but in that case you should be more cautious in your interpretations of others.

The other comment you made relies on assuming that the current mainstream conception of mathematics is hopelessly wrong. This is not a position you have ever successfully justified, or have even come close to successfully justifying. Moreover your own alternative framework is hopelessly inadequate for modern science, offers no computational advantages generally speaking, and seems to require rejecting much of modern science (none of which you seem to have any grasp of) as a necessary condition.

In short it is a tapestry of rubbish mixed with the odd bit of trivia.

Moreover, if people want to see a pre-modern approach to number, they can just go to Euler's charming book 'Elements of Algebra', which is a better piece of work on the whole, even though it could be improved. If they want something more introductory and charming than Euler's work, they should look at the book 'Arithmetic' by Paul Lockhart.

Both myself and others have fairly reviewed much of your work. Much of it is not worth studying. A few small bits can be taken from it as minor curiosities:

1) the secant line approach of your 'new calculus' can handle a very small subset of elementary problems, but runs out of steam quickly and cannot give the analytic notions needed for remotely advanced work (difficulties with points of inflection of simple algebraic functions of one variable are the first sign of deeper problems). It resembles 16th century pre-limit methods, whose shortcomings were part of the motivation for calculus in the first place. See for example this charming 25 minute video by Professor Jeremy Gray, an internationally respected mathematics historian:

https://www.youtube.com/watch?v=ObPg3ki9GOI

As such your secant approach might be useful for illustrating the limitations of pre-limit methods for beginners (although it is somewhat redundant for that purpose given what is shown in the video).

2) Daniel Grace has highlighted an observation of yours concerning cubic functions (I came across this idly glancing through past comments on sci.math):

https://drive.google.com/file/d/1tO66F08uEyuAfucPXTINtGIqdQwFFCaJ/view

Now a sensible person (either without NPD or who had faced up to the fact they had NPD and tried to compensate for this fact) might have tried to find out of the secant method had been exactly discovered before and if not, perhaps try to put together a short essay considering why the method had not been highlighted before and used alongside other pre-limit techniques in the 16th century. Not an important topic, merely a minor curiosity for those interested in the period, but better than nothing. A sensible person would also have thanked Mr Grace for highlighting the cubic property and perhaps tried to check if it had ever been noticed before. If it hadn't been noticed before, maybe publish it. If it had, take some pride in having re-discovered an already noted result. You after all an amateur mathematician rather than a professional researcher.

But you are not sensible. You cannot settle for having made some quirky, but very limited, observations; you instead want to have created a revolutionary general approach to mathematics and want to be admired for such. A delirious aspiration given your lack of background (you don't know enough about mathematical physics to realise how inadequate your approach is even in principle).

Moreover you seem to believe that you have succeeded: a demonstrably false notion, and so pathologically wrong it is hard to know where to start.

Moreover you want to be regarded favorably compared to historically important mathematicians, without having done anything to merit such. So rather than putting in the work to earn the acclaim positively, you instead compensate by insulting the mathematicians and mathematical physicists whose accomplishments you know little about and whose work you probably couldn't understand if required to read it; Lebesgue, Erdos, Euler, Hilbert, Noether Einstein, ... the list could go on. What do you have to offer that compares with what they produced? What problems of importance can be solved, that weren't already solvable generations ago and with far more powerful methods? None of course. But that's okay, simply calling these great minds idiots is more than sufficient as rebuttal. Chuckle.

I suspect NPD as the underlying reason, for which you have my pity if so, but not my silence.

Have a wonderful day.
QB

Remain Calm and Keep Loving Real Analysis

On Friday, 2 July 2021 at 04:59:35 UTC-4, Quantum Bubbles aka ross.pro...@gmx.com wrote:
> On Friday, July 2, 2021 at 1:47:16 AM UTC+1, Eram semper recta wrote:
>
> "Look carefully ... there has not been a single attempt to refute what I claim."

> In one comment you make a false insinuation concerning logical correctness.

If assertions were true, then logical correctness has no value.
Your above assertion is merely that - an assertion.

<Usual drivel which I will not dignify with a response>

> 2) Daniel Grace has highlighted an observation of yours concerning cubic functions (I came across this idly glancing through past comments on sci.math):
>
> https://drive.google.com/file/d/1tO66F08uEyuAfucPXTINtGIqdQwFFCaJ/view

You incorrigible moron! Daniel Grace misunderstood the theorem which has a condition in it. It's called paying attention to detail, you fucking idiot! Grace has sent me several emails since then apologising for his mistake.

The theorem is not a property of cubic functions, but of any function that meets that condition. What this means, moron, is that it will not hold for all functions - as expected. LMAO.

<drivel>

So once again, you've been slapped quite brutally, but I somehow doubt you've learned anything. I know you are obsessed with me. Most people are mystified because geniuses are mysterious to Plebeians like you.

If you really want me to talk to you and educate you, then try addressing the OP. Everything else you say is worthless drivel. Writing diatribes only makes you look stupid - just like your fellow moron Alan McKenzie.

On Friday, 2 July 2021 at 07:57:56 UTC-4, Eram semper recta wrote:
> On Friday, 2 July 2021 at 04:59:35 UTC-4, Quantum Bubbles aka ross.pro...@gmx.com wrote:
> > On Friday, July 2, 2021 at 1:47:16 AM UTC+1, Eram semper recta wrote:
> >
> > "Look carefully ... there has not been a single attempt to refute what I claim."
>
> > In one comment you make a false insinuation concerning logical correctness.
> If assertions were true, then logical correctness has no value.
> Your above assertion is merely that - an assertion.
>
> <Usual drivel which I will not dignify with a response>
> > 2) Daniel Grace has highlighted an observation of yours concerning cubic functions (I came across this idly glancing through past comments on sci.math):
> >
> > https://drive.google.com/file/d/1tO66F08uEyuAfucPXTINtGIqdQwFFCaJ/view
> You incorrigible moron! Daniel Grace misunderstood the theorem which has a condition in it. It's called paying attention to detail, you fucking idiot! Grace has sent me several emails since then apologising for his mistake.
>
> The theorem is not a property of cubic functions, but of any function that meets that condition. What this means, moron, is that it will not hold for all functions - as expected. LMAO.
>
> <drivel>
>
> So once again, you've been slapped quite brutally, but I somehow doubt you've learned anything. I know you are obsessed with me. Most people are mystified because geniuses are mysterious to Plebeians like you.
>
> If you really want me to talk to you and educate you, then try addressing the OP. Everything else you say is worthless drivel. Writing diatribes only makes you look stupid - just like your fellow moron Alan McKenzie.

Students:

The theorem which Daniel Grace supposedly disproved is this one:

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

***IF*** (x,f(x)) is any point on curve f(x) ***AND*** the integral of f from x-delta to x+delta with respect to dx is equal to f(x) x 2(delta), then f(x) is the y ordinate of the inflection point (x,f(x)), because f(x) is also an arithmetic mean. Note that delta must be very small. One cannot cross another inflection point or even a local min or max point.

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

As you can see once again, failure to pay attention to detail is a common trait of mainstream idiots. Their stupidity is the bane of my existence.

On Friday, July 2, 2021 at 12:57:56 PM UTC+1, Eram semper recta wrote:

"You incorrigible moron! Daniel Grace misunderstood the theorem which has a condition in it. It's called paying attention to detail, you fucking idiot! Grace has sent me several emails since then apologising for his mistake."

"The theorem is not a property of cubic functions, but of any function that meets that condition. What this means, moron, is that it will not hold for all functions - as expected. LMAO."

I am sure he was on his knees begging for forgiveness. Or perhaps not. But anyway, if it holds of cubic functions then it is a property of cubic functions. That doesn't prevent it from being a property of a wider class (If we count signed areas and signed heights then trivially a similar thing applies to the points of inflection on sin(x), but any high school student that thinks about integration would know that example). I made no claims about a more general result, other than that you had not discovered anything revolutionary (which is the case), I merely said Daniel Grace highlighted a property of cubics that he came across in your work.

Oh, and by the way, in your response to Daniel Grace you actually said:

"The "article" you wrote is utter rubbish, you pathetic moronic crank. It is you who don't know or understand what you are doing. The theorem works for any function, but how can a baboon like you know."

It's not clear from the video of yours, that Daniel Grace refers to, as to what the condition of applicability is supposed to be for that area formula.. It doesn't apply to the quartic:

f(x) = x^4 - 2x^2 + 1 (non-stationary point of inflection at x = 4/9)

on the interval about x = 4/9 of:

(4/9) - ((3/4) - (sqrt(3))/3) to (4/9) + ((3/4) - (sqrt(3))/3)

The value I get from your formula is approximately 0.153, whereas the definite integral over that interval gives an approximate value of 0.220. So Daniel Grace is correct that it doesn't apply to all quartics. I chose this quartic and the interval carefully so that they didn't have special properties (like containing stationary points or other points of inflection). So what would the general conditions of applicability be beyond the cubic case?

In the unlikely event Daniel Grace is reading this, he might enjoy reading about some investigations into quirky relationships that can arise in quartics with inflection points:

https://www.maa.org/sites/default/files/pdf/cms_upload/Totland200956041.pdf

Anyway...

"So once again, you've been slapped quite brutally..."

Swing and a miss actually.

"Most people are mystified because geniuses are mysterious to Plebeians like you."

You are not a genius Mr Gabriel, at least not in mathematics (perhaps you would have a great talent for gardening or photography or interpersonal skills or something...). You are a hobbyist, who has an enthusiasm for certain elementary parts of mathematics. Nothing remotely wrong with that in itself.. You might occasionally discover something curious. But it is very rare for a hobbyist to make a significant breakthrough given the advanced state of mathematics.

Gauss was a genius. Erdos was a genius. Poincare was a genius. You are not such a genius. An IQ of 115-118 ... possibly. Attended university, at least for the first year, ... possibly.
"If you really want me to talk to you and educate you, then try addressing the OP. Everything else you say is worthless drivel. Writing diatribes only makes you look stupid - just like your fellow moron Alan McKenzie."

I try to take the view sometimes ascribed to Leibniz that anyone capable of learning will find something to learn from anyone else. But we have seen enough of your output to know I would likely be better off speaking to almost any recent graduate instead. It is really with regards to psychology, and to some extent with regards to my ethical beliefs that there remains some marginal interest here.

Have a wonderful day
QB

Remain Calm and Keep Loving Real Analysis

On Friday, 2 July 2021 at 13:28:28 UTC-4, ross.pro...@gmx.com wrote:
> On Friday, July 2, 2021 at 12:57:56 PM UTC+1, Eram semper recta wrote:
>
> "You incorrigible moron! Daniel Grace misunderstood the theorem which has a condition in it. It's called paying attention to detail, you fucking idiot! Grace has sent me several emails since then apologising for his mistake.."
>
> "The theorem is not a property of cubic functions, but of any function that meets that condition. What this means, moron, is that it will not hold for all functions - as expected. LMAO."
> I am sure he was on his knees begging for forgiveness. Or perhaps not. But anyway, if it holds of cubic functions then it is a property of cubic functions. That doesn't prevent it from being a property of a wider class (If we count signed areas and signed heights then trivially a similar thing applies to the points of inflection on sin(x), but any high school student that thinks about integration would know that example). I made no claims about a more general result, other than that you had not discovered anything revolutionary (which is the case), I merely said Daniel Grace highlighted a property of cubics that he came across in your work.
>
> Oh, and by the way, in your response to Daniel Grace you actually said:
>
> "The "article" you wrote is utter rubbish, you pathetic moronic crank. It is you who don't know or understand what you are doing. The theorem works for any function, but how can a baboon like you know."
>
> It's not clear from the video of yours, that Daniel Grace refers to, as to what the condition of applicability is supposed to be for that area formula. It doesn't apply to the quartic:
>
> f(x) = x^4 - 2x^2 + 1 (non-stationary point of inflection at x = 4/9)
>
> on the interval about x = 4/9 of:
>
> (4/9) - ((3/4) - (sqrt(3))/3) to (4/9) + ((3/4) - (sqrt(3))/3)
>
> The value I get from your formula is approximately 0.153, whereas the definite integral over that interval gives an approximate value of 0.220. So Daniel Grace is correct that it doesn't apply to all quartics. I chose this quartic and the interval carefully so that they didn't have special properties (like containing stationary points or other points of inflection). So what would the general conditions of applicability be beyond the cubic case?
>
> In the unlikely event Daniel Grace is reading this, he might enjoy reading about some investigations into quirky relationships that can arise in quartics with inflection points:
>
> https://www.maa.org/sites/default/files/pdf/cms_upload/Totland200956041.pdf
>
> Anyway...
>
> "So once again, you've been slapped quite brutally..."
>
> Swing and a miss actually.
> "Most people are mystified because geniuses are mysterious to Plebeians like you."
> You are not a genius Mr Gabriel, at least not in mathematics (perhaps you would have a great talent for gardening or photography or interpersonal skills or something...). You are a hobbyist, who has an enthusiasm for certain elementary parts of mathematics. Nothing remotely wrong with that in itself. You might occasionally discover something curious. But it is very rare for a hobbyist to make a significant breakthrough given the advanced state of mathematics.
>
> Gauss was a genius. Erdos was a genius. Poincare was a genius. You are not such a genius. An IQ of 115-118 ... possibly. Attended university, at least for the first year, ... possibly.
> "If you really want me to talk to you and educate you, then try addressing the OP. Everything else you say is worthless drivel. Writing diatribes only makes you look stupid - just like your fellow moron Alan McKenzie."
> I try to take the view sometimes ascribed to Leibniz that anyone capable of learning will find something to learn from anyone else. But we have seen enough of your output to know I would likely be better off speaking to almost any recent graduate instead. It is really with regards to psychology, and to some extent with regards to my ethical beliefs that there remains some marginal interest here.
>
> Have a wonderful day
> QB
>
> Remain Calm and Keep Loving Real Analysis

Students:

As you can all see, there is no substance at all here. What we have is just another sci.math troll who constantly makes promises that he will quit responding but continues to do so with only one goal - to throw you off. Arguing with this cowardly anonymous fool just takes up time better spent elsewhere.

You would be better off ignoring everything it writes.

On Friday, July 2, 2021 at 11:30:56 PM UTC+1, Eram semper recta wrote:
> On Friday, 2 July 2021 at 13:28:28 UTC-4, ross.pro...@gmx.com wrote:
> > On Friday, July 2, 2021 at 12:57:56 PM UTC+1, Eram semper recta wrote:
> >
> > "You incorrigible moron! Daniel Grace misunderstood the theorem which has a condition in it. It's called paying attention to detail, you fucking idiot! Grace has sent me several emails since then apologising for his mistake."
> >
> > "The theorem is not a property of cubic functions, but of any function that meets that condition. What this means, moron, is that it will not hold for all functions - as expected. LMAO."
> > I am sure he was on his knees begging for forgiveness. Or perhaps not. But anyway, if it holds of cubic functions then it is a property of cubic functions. That doesn't prevent it from being a property of a wider class (If we count signed areas and signed heights then trivially a similar thing applies to the points of inflection on sin(x), but any high school student that thinks about integration would know that example). I made no claims about a more general result, other than that you had not discovered anything revolutionary (which is the case), I merely said Daniel Grace highlighted a property of cubics that he came across in your work.
> >
> > Oh, and by the way, in your response to Daniel Grace you actually said:
> >
> > "The "article" you wrote is utter rubbish, you pathetic moronic crank. It is you who don't know or understand what you are doing. The theorem works for any function, but how can a baboon like you know."
> >
> > It's not clear from the video of yours, that Daniel Grace refers to, as to what the condition of applicability is supposed to be for that area formula. It doesn't apply to the quartic:
> >
> > f(x) = x^4 - 2x^2 + 1 (non-stationary point of inflection at x = 4/9)
> >
> > on the interval about x = 4/9 of:
> >
> > (4/9) - ((3/4) - (sqrt(3))/3) to (4/9) + ((3/4) - (sqrt(3))/3)
> >
> > The value I get from your formula is approximately 0.153, whereas the definite integral over that interval gives an approximate value of 0.220. So Daniel Grace is correct that it doesn't apply to all quartics. I chose this quartic and the interval carefully so that they didn't have special properties (like containing stationary points or other points of inflection). So what would the general conditions of applicability be beyond the cubic case?
> >
> > In the unlikely event Daniel Grace is reading this, he might enjoy reading about some investigations into quirky relationships that can arise in quartics with inflection points:
> >
> > https://www.maa.org/sites/default/files/pdf/cms_upload/Totland200956041..pdf
> >
> > Anyway...
> >
> > "So once again, you've been slapped quite brutally..."
> >
> > Swing and a miss actually.
> > "Most people are mystified because geniuses are mysterious to Plebeians like you."
> > You are not a genius Mr Gabriel, at least not in mathematics (perhaps you would have a great talent for gardening or photography or interpersonal skills or something...). You are a hobbyist, who has an enthusiasm for certain elementary parts of mathematics. Nothing remotely wrong with that in itself. You might occasionally discover something curious. But it is very rare for a hobbyist to make a significant breakthrough given the advanced state of mathematics.
> >
> > Gauss was a genius. Erdos was a genius. Poincare was a genius. You are not such a genius. An IQ of 115-118 ... possibly. Attended university, at least for the first year, ... possibly.
> > "If you really want me to talk to you and educate you, then try addressing the OP. Everything else you say is worthless drivel. Writing diatribes only makes you look stupid - just like your fellow moron Alan McKenzie."
> > I try to take the view sometimes ascribed to Leibniz that anyone capable of learning will find something to learn from anyone else. But we have seen enough of your output to know I would likely be better off speaking to almost any recent graduate instead. It is really with regards to psychology, and to some extent with regards to my ethical beliefs that there remains some marginal interest here.
> >
> > Have a wonderful day
> > QB
> >
> > Remain Calm and Keep Loving Real Analysis
> Students:
>
> As you can all see, there is no substance at all here. What we have is just another sci.math troll who constantly makes promises that he will quit responding but continues to do so with only one goal - to throw you off. Arguing with this cowardly anonymous fool just takes up time better spent elsewhere.
>
> You would be better off ignoring everything it writes.

Hello Mr Gabriel,

I was actually in the process of posting an amendment to my previous comment which I hope helps a little. It reads as below:

When I posted my previous comment I had not yet seen Mr Gabriel's latest comment from a few hours previously (I got called away from my computer for a long time after beginning my response). If I had seen his follow-up comment, then the content of my response would have been somewhat different, so I will correct it accordingly here.

I had stated the following:

"I am sure he was on his knees begging for forgiveness. Or perhaps not. But anyway, if it holds of cubic functions then it is a property of cubic functions. That doesn't prevent it from being a property of a wider class (If we count signed areas and signed heights then trivially a similar thing applies to the points of inflection on sin(x), but any high school student that thinks about integration would know that example). I made no claims about a more general result, other than that you had not discovered anything revolutionary (which is the case), I merely said Daniel Grace highlighted a property of cubics that he came across in your work. "

"It's not clear from the video of yours, that Daniel Grace refers to, as to what the condition of applicability is supposed to be for that area formula. It doesn't apply to the quartic:

f(x) = x^4 - 2x^2 + 1 (non-stationary point of inflection at x = 4/9)
on the interval about x = 4/9 of:
(4/9) - ((3/4) - (sqrt(3))/3) to (4/9) + ((3/4) - (sqrt(3))/3)
The value I get from your formula is approximately 0.153, whereas the definite integral over that interval gives an approximate value of 0.220. So Daniel Grace is correct that it doesn't apply to all quartics. I chose this quartic and the interval carefully so that they didn't have special properties (like containing stationary points or other points of inflection). So what would the general conditions of applicability be beyond the cubic case?"

This response however assumes that Mr Gabriel's intention in his video is clearly stated, which is what Daniel Grace seems to have assumed. What Grace seems to think he was refuting was the claim that being a point of inflection on a smooth curve was a sufficient condition for the area formula to apply to symmetric width intervals about the x-coordinate of the point of inflection in the general case rather than just the cubic case.

However Mr Gabriel has now posted the following:

***IF*** (x,f(x)) is any point on curve f(x) ***AND*** the integral of f from x-delta to x+delta with respect to dx is equal to f(x) x 2(delta), then f(x) is the y ordinate of the inflection point (x,f(x)), because f(x) is also an arithmetic mean. Note that delta must be very small. One cannot cross another inflection point or even a local min or max point.

[It probably also helps to keep in mind that Mr Gabriel isn't concerned with areas under straight lines]

Which changes the interpretation to be given. I can see why Daniel Grace interprets Mr Gabriel in the previous way, because that is probably how the majority of viewers (if not all of them) would do so given both what he says at certain points in the video and what is displayed in a summary box near the end of it. Mr Gabriel does additionally add that he claims only points of inflection have this property, however this is an additional comment in the summary box and doesn't read as the main claim. (Might be best to edit the video to clarify, Mr Gabriel as your intended meaning isn't remotely clear in that case).

Anyway that is the only amendment I feel the need to make to my comment at the present time.

Have a wonderful day
QB

Remain Calm and Keep Loving Real Analysis

On Thursday, 1 July 2021 at 10:39:14 UTC-4, Eram semper recta wrote:
> The incorrigible morons of mainstream academia define an "irrational number" as:
>
> "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
>
> And then this:
>
> The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
>
> In other words π = C : 2r
>
> However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
>
> By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
>
> Learn what is a number in mathematics exactly:
>
> https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
>
> Students:
>
> The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
>
> Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
>
> At the Mathworld link(https://mathworld.wolfram.com/Ratio.html#:~:text=The%20ratio%20of%20two%20numbers,is%20equivalent%20to%20the%20quotient%20.), the ratio is defined to be a *fraction* of two numbers (numerator and denominator), but neither circumference nor diameter are necessarily ***numbers***.
>
> See what I mean by paying attention to detail my dear students? :)
>
> Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed.

Students:

So you see here how mainstream academics pay no attention to concepts such as ratio, fraction, etc.

For in one definition they will talk about a ratio as being a comparison between two magnitudes such as circumference : diameter and in another they will talk about a ratio as a fraction.

Clearly they are confused. The concept of number is most important in mathematics. Euclid wrote 6 books before he even got to defining the abstract unit in book 7.

Mathematics is the science of measure and number.

On Saturday, 3 July 2021 at 08:55:59 UTC-4, Eram semper recta wrote:
> On Thursday, 1 July 2021 at 10:39:14 UTC-4, Eram semper recta wrote:
> > The incorrigible morons of mainstream academia define an "irrational number" as:
> >
> > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> >
> > And then this:
> >
> > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> >
> > In other words π = C : 2r
> >
> > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> >
> > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> >
> > Learn what is a number in mathematics exactly:
> >
> > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> >
> > Students:
> >
> > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> >
> > Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
> >
> > At the Mathworld link(https://mathworld.wolfram.com/Ratio.html#:~:text=The%20ratio%20of%20two%20numbers,is%20equivalent%20to%20the%20quotient%20.), the ratio is defined to be a *fraction* of two numbers (numerator and denominator), but neither circumference nor diameter are necessarily ***numbers***.
> >
> > See what I mean by paying attention to detail my dear students? :)
> >
> > Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed.
> Students:
>
> So you see here how mainstream academics pay no attention to concepts such as ratio, fraction, etc.
>
> For in one definition they will talk about a ratio as being a comparison between two magnitudes such as circumference : diameter and in another they will talk about a ratio as a fraction.
>
> Clearly they are confused. The concept of number is most important in mathematics. Euclid wrote 6 books before he even got to defining the abstract unit in book 7.
>
> Mathematics is the science of measure and number.

The difference between a ratio and a fraction is that a fraction is a *number*. A ratio is NOT a number.

On Thursday, July 1, 2021 at 9:05:56 PM UTC-4, mitchr...@gmail.com wrote:
> On Thursday, July 1, 2021 at 7:39:14 AM UTC-7, Eram semper recta wrote:
> > The incorrigible morons of mainstream academia define an "irrational number" as:
> >
> > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> >
> > And then this:
> >
> > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> >
> > In other words π = C : 2r
> >
> > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> It is two quantities that operationally divide. A fraction is the same division operation.
> The round formula needs measurement first...
> >
> > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> >
> > Learn what is a number in mathematics exactly:
> >
> > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> >
> > Students:
> >
> > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> >
> > Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
> They share a sameness as a division operation of two quantities you moron....
>
> Mitchell Raemsch.

Yeah, and the rectum has already denied that there is any division going on in what he calls the 'vinculum'.
I have to grant him that he has attempted his own interpretation of mathematics, but we can all see that ultimately he is chasing his own tail around and around here. Every time he claims a sealed argument is a mistake. It is best to declare the openings as such; provide your best analysis; attack the problems of the standing system; but best of all allow for the possibility of your own mistakes.
That the pi is
3.14159
is a topic of avoidance here. I don't know that any of us should ever destroy the magic of pi. As to what exactly this magic is: is it possibly that it is a junction of mathematics with physics? Isn't this a physical problem? That we bump into number theory along the way is great.

On the problem itself I've been going toward general dimensional analysis so to what degree is the problem framed in its general dimensional form? P3 (the plane) is the first continuous form of the problem. Down in P2 we get just two discrete points at say a unit radius and so the quantity drops out from a continuous length to a discrete count. Down in P1 I suppose we just have zero. So then what is the problem in P4 (Cartesian R^3) if these lower systems are correct? Staying with a pair of unit distance dividers (why a pair?) I suppose there is an argument that the trace goes to infinity. One option here might be to declare that the problem is badly constructed from this general dimensional analysis vantage. Maybe the dividers need revision in general dimension.

On Saturday, 3 July 2021 at 10:07:36 UTC-4, timba...@gmail.com wrote:
> On Thursday, July 1, 2021 at 9:05:56 PM UTC-4, mitchr...@gmail.com wrote:
> > On Thursday, July 1, 2021 at 7:39:14 AM UTC-7, Eram semper recta wrote:
> > > The incorrigible morons of mainstream academia define an "irrational number" as:
> > >
> > > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> > >
> > > And then this:
> > >
> > > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> > >
> > > In other words π = C : 2r
> > >
> > > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> > It is two quantities that operationally divide. A fraction is the same division operation.
> > The round formula needs measurement first...
> > >
> > > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> > >
> > > Learn what is a number in mathematics exactly:
> > >
> > > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> > >
> > > Students:
> > >
> > > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> > >
> > > Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
> > They share a sameness as a division operation of two quantities you moron...
> >
> > Mitchell Raemsch.
> Yeah, and the rectum has already denied that there is any division going on in what he calls the 'vinculum'.

Nothing to deny. The vinculum is part of the name, dumbo.

If one says C/2r, then this means that pi is a *number*. What part of this do you not understand?

C/2r CANNOT be since C and 2r have NO COMMON MEASURE. All you can do is write pi = C : 2r

<rest of the drivel ignored>

> I have to grant him that he has attempted his own interpretation of mathematics, but we can all see that ultimately he is chasing his own tail around and around here. Every time he claims a sealed argument is a mistake. It is best to declare the openings as such; provide your best analysis; attack the problems of the standing system; but best of all allow for the possibility of your own mistakes.
> That the pi is
> 3.14159
> is a topic of avoidance here. I don't know that any of us should ever destroy the magic of pi. As to what exactly this magic is: is it possibly that it is a junction of mathematics with physics? Isn't this a physical problem? That we bump into number theory along the way is great.
>
> On the problem itself I've been going toward general dimensional analysis so to what degree is the problem framed in its general dimensional form? P3 (the plane) is the first continuous form of the problem. Down in P2 we get just two discrete points at say a unit radius and so the quantity drops out from a continuous length to a discrete count. Down in P1 I suppose we just have zero. So then what is the problem in P4 (Cartesian R^3) if these lower systems are correct? Staying with a pair of unit distance dividers (why a pair?) I suppose there is an argument that the trace goes to infinity. One option here might be to declare that the problem is badly constructed from this general dimensional analysis vantage. Maybe the dividers need revision in general dimension.

On Saturday, 3 July 2021 at 11:04:12 UTC-4, Eram semper recta wrote:
> On Saturday, 3 July 2021 at 10:07:36 UTC-4, timba...@gmail.com wrote:
> > On Thursday, July 1, 2021 at 9:05:56 PM UTC-4, mitchr...@gmail.com wrote:
> > > On Thursday, July 1, 2021 at 7:39:14 AM UTC-7, Eram semper recta wrote:
> > > > The incorrigible morons of mainstream academia define an "irrational number" as:
> > > >
> > > > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> > > >
> > > > And then this:
> > > >
> > > > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> > > >
> > > > In other words π = C : 2r
> > > >
> > > > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> > > It is two quantities that operationally divide. A fraction is the same division operation.
> > > The round formula needs measurement first...
> > > >
> > > > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> > > >
> > > > Learn what is a number in mathematics exactly:
> > > >
> > > > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> > > >
> > > > Students:
> > > >
> > > > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> > > >
> > > > Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
> > > They share a sameness as a division operation of two quantities you moron...
> > >
> > > Mitchell Raemsch.
> > Yeah, and the rectum has already denied that there is any division going on in what he calls the 'vinculum'.
> Nothing to deny. The vinculum is part of the name, dumbo.
>
> If one says C/2r, then this means that pi is a *number*. What part of this do you not understand?
>
> C/2r CANNOT be since C and 2r have NO COMMON MEASURE. All you can do is write pi = C : 2r

So Mueckenheim writes:

---------
What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.

How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
---------

No wonder WM fails to understand the concept of number, because from his 5th sentence in the first paragraph, he believes that sentient beings could not realise "number" without a physical universe which is FALSE.

Science deals with measurements of the physical universe, but such measurements are derived from mathematics which is the queen of sciences. Mathematics shows us the way to perform reasonable measurements. It is the ultimate guide to ALL measure and number. Neither π nor √17 are numbers of any kind. These are what the Ancient Greeks realised to be incommensurable magnitudes. That is, they exist only as geometrical concepts without the ability to transfer the same to algebra via an abstract unit.

What no academic before me realised about Euclid's Book 7 and definition 1, is that this is how Euclid defined the abstract UNIT. Don't misunderstand me - Euclid knew and understood full well what he was writing, but he FAILED to express it correctly and the definition cannot be done justice in one vague sentence, but requires 6 books (Book 1 thru 6 of the Elements) and the following articles:

THERE ARE NO AXIOMS OR POSTULATES IN SOUND MATHEMATICS:

https://drive.google.com/file/d/1vlU-PJeIk672bFwZyULD1ASTRFF3jXg8

HOW A GENIUS DISCOVERS THE CONCEPT OF NUMBER:

https://drive.google.com/file/d/1FDxd79p3ZF3pfr8VRDl7R9nqcWeWsdfu

IS π A NUMBER?

https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3

IS THE "REAL NUMBER LINE" REAL?

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

>
> <rest of the drivel ignored>
> > I have to grant him that he has attempted his own interpretation of mathematics, but we can all see that ultimately he is chasing his own tail around and around here. Every time he claims a sealed argument is a mistake. It is best to declare the openings as such; provide your best analysis; attack the problems of the standing system; but best of all allow for the possibility of your own mistakes.
> > That the pi is
> > 3.14159
> > is a topic of avoidance here. I don't know that any of us should ever destroy the magic of pi. As to what exactly this magic is: is it possibly that it is a junction of mathematics with physics? Isn't this a physical problem? That we bump into number theory along the way is great.
> >
> > On the problem itself I've been going toward general dimensional analysis so to what degree is the problem framed in its general dimensional form? P3 (the plane) is the first continuous form of the problem. Down in P2 we get just two discrete points at say a unit radius and so the quantity drops out from a continuous length to a discrete count. Down in P1 I suppose we just have zero. So then what is the problem in P4 (Cartesian R^3) if these lower systems are correct? Staying with a pair of unit distance dividers (why a pair?) I suppose there is an argument that the trace goes to infinity. One option here might be to declare that the problem is badly constructed from this general dimensional analysis vantage. Maybe the dividers need revision in general dimension.

On Monday, July 5, 2021 at 9:00:28 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

>
> THERE ARE NO AXIOMS OR POSTULATES IN SOUND MATHEMATICS:
>

With his bizarre attempts to ban all axioms and postulates from mathematics seems to be hoping that he can get off the hook for failing to derive even the most elementary results in basic arithmetic -- such proofs requires axioms. What a moron!

*********************************************
WARNING TO STUDENTS: Don't become a victim of JG's fake math

JG here claims to have a discovered as 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. What a moron!

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

On Monday, July 5, 2021 at 9:00:28 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

>
> THERE ARE NO AXIOMS OR POSTULATES IN SOUND MATHEMATICS:
>

With his bizarre attempts to ban all axioms and postulates from mathematics, Troll Boy here seems to be hoping that he can get off the hook for failing to derive even the most elementary results in basic arithmetic -- such proofs requires axioms. What a moron!

*********************************************
WARNING TO STUDENTS: Don't become a victim of JG's fake math

JG here claims to have a discovered as 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. What a moron!

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

On Monday, 5 July 2021 at 09:00:28 UTC-4, Eram semper recta wrote:
> On Saturday, 3 July 2021 at 11:04:12 UTC-4, Eram semper recta wrote:
> > On Saturday, 3 July 2021 at 10:07:36 UTC-4, timba...@gmail.com wrote:
> > > On Thursday, July 1, 2021 at 9:05:56 PM UTC-4, mitchr...@gmail.com wrote:
> > > > On Thursday, July 1, 2021 at 7:39:14 AM UTC-7, Eram semper recta wrote:
> > > > > The incorrigible morons of mainstream academia define an "irrational number" as:
> > > > >
> > > > > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> > > > >
> > > > > And then this:
> > > > >
> > > > > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> > > > >
> > > > > In other words π = C : 2r
> > > > >
> > > > > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> > > > It is two quantities that operationally divide. A fraction is the same division operation.
> > > > The round formula needs measurement first...
> > > > >
> > > > > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> > > > >
> > > > > Learn what is a number in mathematics exactly:
> > > > >
> > > > > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> > > > >
> > > > > Students:
> > > > >
> > > > > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> > > > >
> > > > > Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
> > > > They share a sameness as a division operation of two quantities you moron...
> > > >
> > > > Mitchell Raemsch.
> > > Yeah, and the rectum has already denied that there is any division going on in what he calls the 'vinculum'.
> > Nothing to deny. The vinculum is part of the name, dumbo.
> >
> > If one says C/2r, then this means that pi is a *number*. What part of this do you not understand?
> >
> > C/2r CANNOT be since C and 2r have NO COMMON MEASURE. All you can do is write pi = C : 2r
> So Mueckenheim writes:
>
> ---------
> What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.
>
> How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
> ---------
>
> No wonder WM fails to understand the concept of number, because from his 5th sentence in the first paragraph, he believes that sentient beings could not realise "number" without a physical universe which is FALSE.
>
> Science deals with measurements of the physical universe, but such measurements are derived from mathematics which is the queen of sciences. Mathematics shows us the way to perform reasonable measurements. It is the ultimate guide to ALL measure and number. Neither π nor √17 are numbers of any kind. These are what the Ancient Greeks realised to be incommensurable magnitudes. That is, they exist only as geometrical concepts without the ability to transfer the same to algebra via an abstract unit.
>
> What no academic before me realised about Euclid's Book 7 and definition 1, is that this is how Euclid defined the abstract UNIT. Don't misunderstand me - Euclid knew and understood full well what he was writing, but he FAILED to express it correctly and the definition cannot be done justice in one vague sentence, but requires 6 books (Book 1 thru 6 of the Elements) and the following articles:
>
> THERE ARE NO AXIOMS OR POSTULATES IN SOUND MATHEMATICS:
>
> https://drive.google.com/file/d/1vlU-PJeIk672bFwZyULD1ASTRFF3jXg8
>
> HOW A GENIUS DISCOVERS THE CONCEPT OF NUMBER:
>
> https://drive.google.com/file/d/1FDxd79p3ZF3pfr8VRDl7R9nqcWeWsdfu
>
> IS π A NUMBER?
>
> https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3
>
> IS THE "REAL NUMBER LINE" REAL?
>
> https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc
> >
> > <rest of the drivel ignored>
> > > I have to grant him that he has attempted his own interpretation of mathematics, but we can all see that ultimately he is chasing his own tail around and around here. Every time he claims a sealed argument is a mistake. It is best to declare the openings as such; provide your best analysis; attack the problems of the standing system; but best of all allow for the possibility of your own mistakes.
> > > That the pi is
> > > 3.14159
> > > is a topic of avoidance here. I don't know that any of us should ever destroy the magic of pi. As to what exactly this magic is: is it possibly that it is a junction of mathematics with physics? Isn't this a physical problem? That we bump into number theory along the way is great.
> > >
> > > On the problem itself I've been going toward general dimensional analysis so to what degree is the problem framed in its general dimensional form? P3 (the plane) is the first continuous form of the problem. Down in P2 we get just two discrete points at say a unit radius and so the quantity drops out from a continuous length to a discrete count. Down in P1 I suppose we just have zero. So then what is the problem in P4 (Cartesian R^3) if these lower systems are correct? Staying with a pair of unit distance dividers (why a pair?) I suppose there is an argument that the trace goes to infinity. One option here might be to declare that the problem is badly constructed from this general dimensional analysis vantage. Maybe the dividers need revision in general dimension.

Students:

You know a troll when you see him continuing to post drivel even though he never gets any responses. Such is this vile reptile Dan Christensen. Nothing he writes is true and that which is, is taken out of context.

This bastard has been harassing and bullying me for the last 4 years. He will see justice come his way once I find out who he is.

On Monday, July 5, 2021 at 4:53:09 PM UTC+1, Eram semper recta wrote:

"You know a troll when you see him continuing to post drivel even though he never gets any responses. Such is this vile reptile Dan Christensen. Nothing he writes is true and that which is, is taken out of context. This bastard has been harassing and bullying me for the last 4 years. He will see justice come his way once I find out who he is."

Leaving aside the question of what such 'justice' would consist of, surely the true trolls are those who continue to post even when they are repeatedly refuted? As a case in point, to date you have still not been able to demonstrate a failure within the content of mainstream mathematics nor have you demonstrated that your own approach can substitute for it in the realm of mathematical physics: especially quantum mechanics and general relativity. You do accept quantum mechanics and general relativity as the best available scientific theories of nature don't you Mr Gabriel? We know you don't accept evolution despite the overwhelming evidence in its favour.

The only (indirect) point you have ever raised that I would have some significant agreement with was highlighting the essay by Kinsey and Shirley (which I had read years ago), but that concerns pedagogy rather than conceptual validity.

But anyway:

1) Have you yet developed a rigorous derivation of the Euler-Lagrange equation without using limits?

2) As the self-claimed 'greatest mathematician since Archimedes' have you cracked any of the unsolved Erdos problems yet? After all Erdos is generally regarded as the 20th century's greatest number theorist, so if you really understand numbers better than he did...

3) Have you got any proof yet of your claim to be a genius with an IQ over 4 sigma above average?

4) Have you changed your mind on evolution yet?

Have a wonderful day
QB

Remain Calm and Keep Loving Real Analysis
[Recommended Book of the Day: Elementary Differential Geometry, 2e, by Andrew Pressley]

On Monday, July 5, 2021 at 8:53:09 AM UTC-7, Eram semper recta wrote:
> On Monday, 5 July 2021 at 09:00:28 UTC-4, Eram semper recta wrote:
> > On Saturday, 3 July 2021 at 11:04:12 UTC-4, Eram semper recta wrote:
> > > On Saturday, 3 July 2021 at 10:07:36 UTC-4, timba...@gmail.com wrote:
> > > > On Thursday, July 1, 2021 at 9:05:56 PM UTC-4, mitchr...@gmail.com wrote:
> > > > > On Thursday, July 1, 2021 at 7:39:14 AM UTC-7, Eram semper recta wrote:
> > > > > > The incorrigible morons of mainstream academia define an "irrational number" as:
> > > > > >
> > > > > > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> > > > > >
> > > > > > And then this:
> > > > > >
> > > > > > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> > > > > >
> > > > > > In other words π = C : 2r
> > > > > >
> > > > > > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> > > > > It is two quantities that operationally divide. A fraction is the same division operation.
> > > > > The round formula needs measurement first...
> > > > > >
> > > > > > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> > > > > >
> > > > > > Learn what is a number in mathematics exactly:
> > > > > >
> > > > > > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> > > > > >
> > > > > > Students:
> > > > > >
> > > > > > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> > > > > >
> > > > > > Mainstream academics have confused the word ratio with fraction.. The baboons use these interchangeably.
> > > > > They share a sameness as a division operation of two quantities you moron...
> > > > >
> > > > > Mitchell Raemsch.
> > > > Yeah, and the rectum has already denied that there is any division going on in what he calls the 'vinculum'.
> > > Nothing to deny. The vinculum is part of the name, dumbo.
> > >
> > > If one says C/2r, then this means that pi is a *number*. What part of this do you not understand?
> > >
> > > C/2r CANNOT be since C and 2r have NO COMMON MEASURE. All you can do is write pi = C : 2r
> > So Mueckenheim writes:
> >
> > ---------
> > What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.
> >
> > How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
> > ---------
> >
> > No wonder WM fails to understand the concept of number, because from his 5th sentence in the first paragraph, he believes that sentient beings could not realise "number" without a physical universe which is FALSE.
> >
> > Science deals with measurements of the physical universe, but such measurements are derived from mathematics which is the queen of sciences. Mathematics shows us the way to perform reasonable measurements. It is the ultimate guide to ALL measure and number. Neither π nor √17 are numbers of any kind. These are what the Ancient Greeks realised to be incommensurable magnitudes. That is, they exist only as geometrical concepts without the ability to transfer the same to algebra via an abstract unit.
> >
> > What no academic before me realised about Euclid's Book 7 and definition 1, is that this is how Euclid defined the abstract UNIT. Don't misunderstand me - Euclid knew and understood full well what he was writing, but he FAILED to express it correctly and the definition cannot be done justice in one vague sentence, but requires 6 books (Book 1 thru 6 of the Elements) and the following articles:
> >
> > THERE ARE NO AXIOMS OR POSTULATES IN SOUND MATHEMATICS:
> >
> > https://drive.google.com/file/d/1vlU-PJeIk672bFwZyULD1ASTRFF3jXg8
> >
> > HOW A GENIUS DISCOVERS THE CONCEPT OF NUMBER:
> >
> > https://drive.google.com/file/d/1FDxd79p3ZF3pfr8VRDl7R9nqcWeWsdfu
> >
> > IS π A NUMBER?
> >
> > https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3
> >
> > IS THE "REAL NUMBER LINE" REAL?
> >
> > https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc
> > >
> > > <rest of the drivel ignored>
> > > > I have to grant him that he has attempted his own interpretation of mathematics, but we can all see that ultimately he is chasing his own tail around and around here. Every time he claims a sealed argument is a mistake. It is best to declare the openings as such; provide your best analysis; attack the problems of the standing system; but best of all allow for the possibility of your own mistakes.
> > > > That the pi is
> > > > 3.14159
> > > > is a topic of avoidance here. I don't know that any of us should ever destroy the magic of pi. As to what exactly this magic is: is it possibly that it is a junction of mathematics with physics? Isn't this a physical problem? That we bump into number theory along the way is great.
> > > >
> > > > On the problem itself I've been going toward general dimensional analysis so to what degree is the problem framed in its general dimensional form? P3 (the plane) is the first continuous form of the problem. Down in P2 we get just two discrete points at say a unit radius and so the quantity drops out from a continuous length to a discrete count. Down in P1 I suppose we just have zero. So then what is the problem in P4 (Cartesian R^3) if these lower systems are correct? Staying with a pair of unit distance dividers (why a pair?) I suppose there is an argument that the trace goes to infinity. One option here might be to declare that the problem is badly constructed from this general dimensional analysis vantage. Maybe the dividers need revision in general dimension.
> Students:
>
> You know a troll when you see him continuing to post drivel even though he never gets any responses. Such is this vile reptile Dan Christensen. Nothing he writes is true and that which is, is taken out of context.
>
> This bastard has been harassing and bullying me for the last 4 years. He will see justice come his way once I find out who he is.

Is he an hypocrite?
Where you use infinity in that way...
Remember?

Mitchell Raemsch

On Thursday, 1 July 2021 at 10:41:20 UTC-4, Eram semper recta wrote:
> On Thursday, 1 July 2021 at 10:39:14 UTC-4, Eram semper recta wrote:
> > The incorrigible morons of mainstream academia define an "irrational number" as:
> >
> > "An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic." - https://mathworld.wolfram.com/IrrationalNumber.html
> >
> > And then this:
> >
> > The constant π, denoted π, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r.
> >
> > In other words π = C : 2r
> >
> > However, a ratio is NOT a number! This means it cannot be written as C / 2r because C : 2r and C/2r are two completely different things.
> >
> > By the mainstream definition, π is an "irrational number", therefore it cannot be written as C / 2r because C is a "numerator" and 2r is a "denominator" meaning both are integers or rational numbers.
> >
> > Learn what is a number in mathematics exactly:
> >
> > https://drive.google.com/file/d/1kU_QXEIT28efbQ2URrJydQrmtvihSRqq
> >
> > Students:
> >
> > The stupidity of mainstream academics and their consistent failure to pay attention to detail has resulted in the garbage you now are forced to learn at school.
> >
> > Mainstream academics have confused the word ratio with fraction. The baboons use these interchangeably.
> >
> > At the Mathworld link(https://mathworld.wolfram.com/Ratio.html#:~:text=The%20ratio%20of%20two%20numbers,is%20equivalent%20to%20the%20quotient%20.), the ratio is defined to be a *fraction* of two numbers (numerator and denominator), but neither circumference nor diameter are necessarily ***numbers***.
> >
> > See what I mean by paying attention to detail my dear students? :)
> >
> > Mainstream academics are incorrigibly stupid morons who cannot and more importantly will not be fixed.
> So in one link, the baboons who run Mathworld say an "irrational number" cannot be written as a *fraction* and in another link, they say that pi can be written as a fraction of two numbers. Which is it? :)

According to the fools of the cult that is mainstream academia, an "irrational number" is one that cannot be written as fraction of two integers, but it can be written as a fraction of two "real numbers"? LMAO.

Circularity is the primary doctrine of the Church of Academia.

>
> Tsk, tsk.