Calculus is 100% pure geometry.

[Eram semper recta]

Calculus is 100% pure geometry. What you have in mainstream calculus is the result of centuries of inability and incompetence to produce a rigorous formulation.

But do not despair! I have done it:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO


Preempting anonymous coward and king troll of sci.math Dan Christensen who will no doubt spam my threads:


> "There are no points on a line."

Lie. I never said that. What I did say is that a line does not consists of points. When we talk about points on a line, we really mean distances that are indicated much like road signs do for distances travelled along a road.

A line is one of innumerable distances between any two points.
A straight line is the shortest distance between two points.


> "Pi is NOT a number of ANY kind!"

True. Pi is merely a symbol for an incommensurable magnitude - apparently a concept too advanced for an imbecile like Dan Christensen.

> "1/2 not equal to 2/4"

Lie. I have NEVER said this. What I have talked about is the difference in the process of measure.
What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.

There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:

_ / _ _
_ _ / _ _ _ _

The length _ is not equal to the length _ _ .

> “1/3 does NOT mean 1 divided by 3 and never has meant that”

True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

Also, my article on pi not being a number of any kind:

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

The true story of how we got numbers:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

No such thing as a "real number" or a "real number line":

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

There is no valid construction of "real number" - it's a myth:

https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU


> "3 =< 4 is nonsense.”

True. In mathematics, it is called an invalid disjunction.

3 <= 4 means EITHER 3 < 4 OR 3 = 4

Actually, there is no "OR" part, so the logical disjunction is invalid.

> "Zero is not a number."

True. While not a number of any kind, it is very useful in mathematics.

https://drive.google.com/file/d/1w2tt7IgoIu-ychDCoYi-4jOAzToy0ViM

> "0 is not required at all in mathematics, just like negative numbers."

Half-truth. While negative numbers are not required in mathematics, they are extremely useful.

> “There is no such thing as an empty set.”

True. Even the father of all mainstream mathematical cranks rejected the idea of empty set. But let's not go too far ... there isn't even a definition of "set" in set theory!

https://youtu.be/KvxjOMW6Q9w

https://youtu.be/1CcSsOG0okg

> “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)

True. These are propositions that are implied by the given equations. For example, my historic geometric identity states:

[f(x+h)-f(x)]/h = dy/dx + Q(x,h)

And so, f(x+h)-f(x)]/h <=> dy/dx + Q(x,h)

The theorem:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

How it provides a rigorous definition of integral for the flawed mainstream calculus:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

The day will come when this vicious anonymous troll Dan Christensen is convicted in a court of law.

Download for free the most important mathematics book ever written:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

The New Calculus is proof that you CAN DO calculus without the use of LIMIT THEORY.

Don't believe me? Study it. You will be pleasantly surprised.

I am a genius and the greatest mathematician alive today.

[Dan Christensen]

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

On Monday, September 6, 2021 at 6:18:16 AM UTC-4, I am Super Rectum (aka John Gabriel (JG), Troll Boy) wrote:

> Calculus is 100% pure geometry. What you have in mainstream calculus is the result of centuries of inability and incompetence to produce a rigorous formulation.
>

What YOU yourself have, Troll Boy, is a goofy little system that just doesn't work.

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. What a moron!

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. Again, 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

[markus...@gmail.com]

innumerable more like uncountable

[Ross A. Finlayson]

On Monday, September 6, 2021 at 8:38:01 AM UTC-7, markus...@gmail.com wrote:
> innumerable more like uncountable


Copy-pasting more like spam. (Troll more like bum.)

Excuse, Mann kann nur ein Kleiner gesprechern, aber die Anglosich
ist eine grosser Wortschatz.

Mathematics is very geometrical, and it's fair that geometry is
very fundamental, where sets and partitions are fundamental,
categories or types ..., functions, models, and usually according
to "least action" the simple, geometry is both fundamental and
emergent.

With respect to modern mathematics there's a not unusual
classical and even pre-classical notion of a spiral space-filling
curve as a natural continuum, which works out defining geometry
as that Euclid's are emergent properties besides when in a theory
of Euclid's they're axioms.

Then, "calculus as pure geometry" has a meaning and even a
way to formalize, from lesser principles, what's usually arrived
at these days as separately geometry (which is first Euclidean)
and analysis (which is a means of arriving at a model of real
numbers by closing the field with axiomatizing LUB and measure 1.0)
that this sort of model of mathematical primitives arrives at both.

So, at least some modern efforts in foundations, arrive at
more from less, and it's totally usual.

[mitchr...@gmail.com]

What does calculus say about round?
What about original measurement?
What does a radius in geometry mean
as calculus?

Mitchell Raemsch

[Dan Christensen]

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

On Monday, September 6, 2021 at 6:18:16 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

> > "1/2 not equal to 2/4"
> Lie. I have NEVER said this.

A direct quote from October 22, 2017 here at sci.math

> What I have talked about is the difference in the process of measure.
> What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
> 2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.
>
> There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:
>

When will you learn, Troll Boy? 1/2 is ALWAYS EQUAL to 2/4.

[snip]

> > “1/3 does NOT mean 1 divided by 3 and never has meant that”

> True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail...

If you can't dazzle them brilliance, baffle them with bullshit, right, Troll Boy?

> > "3 =< 4 is nonsense.”
> True. In mathematics, it is called an invalid disjunction.
>
> 3 <= 4 means EITHER 3 < 4 OR 3 = 4
>

Since 3 < 4, it is true that 3 < 4 or 3 = 4 even though 3 =4 is false. Nothing "invalid" about it, Troll Boy.

See: https://en.wikipedia.org/wiki/Truth_table#Logical_disjunction_(OR)

[snip]

> > "Zero is not a number."
> True. While not a number of any kind, it is very useful in mathematics.
>

It really is a number, Troll Boy. Deal with it.

> > "0 is not required at all in mathematics, just like negative numbers."

> Half-truth.

Nope. Completely false. Both 0 and negative numbers are required in mathematics.

> While negative numbers are not required in mathematics, they are extremely useful.

<yawn!>

> > “There is no such thing as an empty set.”

> True.

Umm... What about the set of all your brilliant mathematical discoveries? Empty.

[snip]

> > “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions”

> True.

Nope. The biconditional is logical connective. See https://en.wikipedia.org/wiki/Logical_biconditional

3 is not a statement that is true or false. 3 is a number. So 3 <=> 2+1 would be an error in syntax. Deal with it, Troll Boy.


[snip]

> > 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

Also, all direct quotes from you, Troll Boy. To the extent that you will be remembered at all, history will not be kind to you. Time to cut your losses and move on Troll Boy.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com

Visit my Math Blog at http://www.dcproof.wordpress.com

[Eram semper recta]

Gibberish again?

[markus...@gmail.com]

Define "innumerable" in a way that doesn't involve infinity.

[zelos...@gmail.com]

>Calculus is 100% pure geometry. What you have in mainstream calculus is the result of centuries of inability and incompetence to produce a rigorous formulation.

Given that calculus deals with C^n[A] for A c R^m while geometry deals with R^2 or R^3 they are quite different.

>I am a genius and the greatest mathematician alive today.

And you say shit like

>> "Zero is not a number."
>
>True. While not a number of any kind, it is very useful in mathematics.

Only an idiot says this.

[Eram semper recta]

<<Cannot be counted.>>

Webster: too many to be counted.

See? And this is why it pays to always consult the dictionary!

<<innumerable>> is the opposite of <<numerable>>.

[zelos...@gmail.com]

What an amazing mathematical definition, so clear and perfect /s

[markus...@gmail.com]

What does "too many to be counted" mean?

[Eram semper recta]

It means that if you could live forever and do nothing else but count, then you would still never finish.

[markus...@gmail.com]

So your definition is dependent on life existing?

[New Age Prophet]

Shut up moron. You are too stupid to continue this discussion. Get an education! Learn how to read English while you're at it.

[Ross A. Finlayson]

"Geometry is motion".

[markus...@gmail.com]

Why just not answer the question? If something has to count something in order for it exist, wouldn't that make numbers finitely many? How can you ratify anything finitely largely enough if the time, energy and space you will use and experience is finite?

I'd say the last number is 100000000000000000000000000000000000000, because I wouldn't literally be able to count higher than that in all my life. Hence there is no larger natural number.

[mitchr...@gmail.com]

But what if the universe dies like scientists say?
Religion knows better.
One day it will be so old that its age cannot
be written down.

Mitchell Raemsch

[Python]

smitchTheV...@gmail.com schwrote:
...

> But what if the universe dies like scientists say?
> Religion knows better.

Which one? Why?

[Dan Christensen]

Jeez, yer dumb, Troll Boy. In mathematics, a set X is said to be uncountable (or innumerable) iff there does not does not exist an injective function (Google it) f: X --> N.

You haven't also banned all functions, have you, Troll Boy? (HA, HA, HA!!!)

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com

Visit my Math Blog a http://www.dcproof.wordpress.com

[mitchr...@gmail.com]

Science says all stars die.
Religion knows God does not end His universe
because of us.

Mitchell Raemsch

[zelos...@gmail.com]

tisdag 7 september 2021 kl. 22:13:30 UTC+2 skrev New Age Prophet:

When people ask the "difficult" questions you cannot answer, this is your typical response.

[Eram semper recta]

OH? YOU MEAN LIKE:

What does "too many to be counted" mean?

LMAO. You stupid crank!

[markus...@gmail.com]

Yes, please define that rigorously.

[zelos...@gmail.com]

see, he asks legitimate questions and because they show your stupidity you refuse to answer.

[New Age Prophet]

> see, he asks legitimate questions ...

And if you bother to look here, I actually graced your fellow idiot with a response even though one was not necessary!

https://groups.google.com/g/sci.math/c/ff01YMDONj8/m/MWRXLxdbAAAJ

The dictionary defines the meaning of innumerable very clearly:

https://www.merriam-webster.com/dictionary/innumerable

innumerable: too many to be numbered

Now if you cannot understand that, you should probably go back to primary school.

<PLONK>

[Dan Christensen]

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

On Wednesday, September 8, 2021 at 12:06:54 PM UTC-4, New Age Prophet (aka John Gabriel (JG), Troll Boy) wrote:

> The dictionary defines the meaning of innumerable very clearly:
>
> https://www.merriam-webster.com/dictionary/innumerable
>
> innumerable: too many to be numbered
>
> Now if you cannot understand that, you should probably go back to primary school.
>

Dictionary definitions are a good starting point for informal discussions, but, as you must know by now, they can be quite useless when it comes to mathematical proofs, e.g. using your "definition" of a number, you cannot even prove that 2+2=4. As far as innumerable (or uncountable) sets go, the dictionary definition is useless for proving, for example, that the power set of N is uncountable. You need to know that a set X is uncountable iff there exists no injective function f: X --> N. In other words, there are more elements in X than there are in N. Get it? Didn't think so. Oh, well...

Really, Troll Boy, you are wasting your time here. If you want to continue discussing higher math with grown-ups, you really must at least get that GED. Don't you think, it is time at your age that you accomplished SOMETHING in your life?

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com

Visit my Math Blog at http://www.dcproof.wordpress.com

[markus...@gmail.com]

What does "too many to be numbered" mean mathematically?

[zelos...@gmail.com]

and his point that for example 10^100 fits that because you cannot reach it in a human lifespan or computers can't even time etc.

Again dictionaries are descriptive, not prescriptive. That is why he asks for you to clearify.

[Eram semper recta]

You see, if you had actually studied Euclid's Elements, you would have known the answer to this question. Hint: n+1

You would have also known that it was not Euclid who defined the tangent line, but Apollonius, the author of conics - a work too advanced for even most mainstream math PhDs today.

Do you feel stupid? It's so because you really are stupid. Your ignorance coupled with your arrogance produces a very foul stench.

Malum scribbled:

" and his point that for example 10^100 fits that because you cannot reach it in a human lifespan or computers can't even time etc.
Again dictionaries are descriptive, not prescriptive. That is why he asks for you to clearify."

Get the following into your thick skull MALUM (means crank):

IF you cannot express your ideas in natural language, THEN you cannot do the same in mathematics or in any other science.

This is why people ask: "What does <something> mean"?

I've pointed out to you and your fellow idiots, that if I give you a definition #^*$&Y@, then you cannot understand it unless it is well defined using a choice of natural language. You cannot learn or understand anything without the use of natural language. YES! That's why you need to refer to a dictionary - it usually contains the current meaning of words. This is why you never understand what is being said because you have so much drivel in your brain that prevents you from thinking clearly.

[Dan Christensen]

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

On Thursday, September 9, 2021 at 1:47:28 AM UTC-4, I am Super Rectum (aka John Gabriel (JG), Troll Boy) wrote:

[snip]

> > What does "too many to be numbered" mean mathematically?
> You see, if you had actually studied Euclid's Elements, you would have known the answer to this question. Hint: n+1
>

If you had actually studied set theory, you would know that a set X is uncountable (or innumerable) iff there exists no injective function f: X --> N. It has nothing to do with Euclid.

[zelos...@gmail.com]

>You see, if you had actually studied Euclid's Elements

It is not the end all be all book.

>Get the following into your thick skull MALUM (means crank):

Look up what Malum means :) It does not mean crank. You are a crank.

>IF you cannot express your ideas in natural language, THEN you cannot do the same in mathematics or in any other science.

You can express it clearer, easier and shorter in FOL without the need to ask questions to clearify.

>I've pointed out to you and your fellow idiots, that if I give you a definition #^*$&Y@, then you cannot understand it unless it is well defined using a choice of natural language.

Using natural languages means it is open for ambiguity, FOL has NO ambiguity to it as it is extremely strict.

>You cannot learn or understand anything without the use of natural language.

Humans need to use natural languages to communicate, but there are reasons why we have in technical fields strict rules and precise words among many things to reduce the issues of it. NOL is a written language we have made to be EXTREMELY clear and have NO ambiguity as to avoid the ambiguities of natural languages.

>YES! That's why you need to refer to a dictionary - it usually contains the current meaning of words.

it describes the common usages, that does not always work when it comes to highly technical fields.

>This is why you never understand what is being said because you have so much drivel in your brain that prevents you from thinking clearly.

I know mathematics and many things more than you. You call anything you do not understand drivel.

[markus...@gmail.com]

A dictionary contains common day uses of a word, not technical uses of a word. A YouTube video named "funny compilation" most likely doesn't mean anything related to GCC and programming at all. Would it be fair to LOGICALLY DESTROY PROGRAMMING WITH FACTS AND LOGIC using this more common usage of the word "compilation"?

[Eram semper recta]

On Thursday, 9 September 2021 at 12:21:47 UTC+3, zelos...@gmail.com wrote:
> >You see, if you had actually studied Euclid's Elements
> It is not the end all be all book.

It is very much the end all and be all book. This is why it is still in use today and the bullshit you are propagating is no longer in fashion.

Klyver scribbled:

"A dictionary contains common day uses of a word, not technical uses of a word."

Not at all. A dictionary contains the meaning of words.

"A YouTube video named "funny compilation" most likely doesn't mean anything related to GCC and programming at all. Would it be fair to LOGICALLY DESTROY PROGRAMMING WITH FACTS AND LOGIC using this more common usage of the word "compilation"?"

I see no analogy whatsoever, only a false analogy which you normally use in your "arguments".

[zelos...@gmail.com]

>It is very much the end all and be all book.

Maybe to you, but not the rest of the world nor to mathematics. It is just a book with history behind it.

>This is why it is still in use today and the bullshit you are propagating is no longer in fashion.

No university, no school, no one uses it today. People read it to see the historical importance of it but that is all it is today.

What Markus and I say is what is used today at universities.

>Not at all. A dictionary contains the meaning of words.

False, again, it is descriptive of usage by people. It does not mean it contains all the technical stuff

[markus...@gmail.com]

That is just wrong. Most dictionaries won't mention programming if you look under "compilation". Why? Because the technical meaning gets left out.

And sometimes dictionaries has some technical words in and leave out others. You won't most likely see a definition of an "open set" in a dictionary.

[Eram semper recta]

On Friday, 10 September 2021 at 13:02:55 UTC+3, markus...@gmail.com wrote:
> fredag 10 september 2021 kl. 06:55:32 UTC+2 skrev Eram semper recta:
> > On Thursday, 9 September 2021 at 12:21:47 UTC+3, zelos...@gmail.com wrote:
> > > >You see, if you had actually studied Euclid's Elements
> > > It is not the end all be all book.
> > It is very much the end all and be all book. This is why it is still in use today and the bullshit you are propagating is no longer in fashion.
> >
> > Klyver scribbled:
> > "A dictionary contains common day uses of a word, not technical uses of a word."
> > Not at all. A dictionary contains the meaning of words.
> > "A YouTube video named "funny compilation" most likely doesn't mean anything related to GCC and programming at all. Would it be fair to LOGICALLY DESTROY PROGRAMMING WITH FACTS AND LOGIC using this more common usage of the word "compilation"?"
> > I see no analogy whatsoever, only a false analogy which you normally use in your "arguments".


> That is just wrong.

Nope. But I'll bite in response to your drivel this time....

> Most dictionaries won't mention programming if you look under "compilation".

Because it is not necessary. Compilation is a general noun that can be used in many contexts.

However, a <<compiler>> is a program that converts instructions into a machine-code or lower-level form so that they can be read and executed by a computer. There is a TECHNICAL ENTRY in the dictionary, so once again, you're an ignorant LIAR.

> Why? Because the technical meaning gets left out.

FALSE. See above.

>
> And sometimes dictionaries has some technical words in and leave out others.

FALSE. You having the typical mindset of a Trump supporter, facts don't mean anything to you. You simply dispense false information along with your co-troll and crank Zelos Malum.

> You won't most likely see a definition of an "open set" in a dictionary.

Not surprising, it's a junk concept that is hardly worth mentioning anywhere.

For all intents and purposes, there is nothing remarkable about either of the intervals (p,q) and [p,q]. It makes you feel smart though, doesn't it? LMAO.

[markus...@gmail.com]

That's the point, "compilation" has far more wide uses than what a compiler does to programming code, Hence this technical usage of the word won't likely show up in a dictionary, The same is true for many math words. Open sets, derivative, topology, functor, contradiction, limit, ... you name it.

So you can't really expect a dictionary to define these words in a technical sense and it doesn't make sense to "try debunking" math by strawmanning the meaning of words.

You should know better than debating semantics.

[Eram semper recta]

It does not matter that every word show up in the dictionary. What matters is that you understand the words which ARE IN the dictionary. Evidently you do not!

<drivel>

[markus...@gmail.com]

It also means a dictionary cannot be an absolute authority on terminology. Ultimately, math words means whatever standard textbokks and the mathematical community want them to mean.

[Eram semper recta]

I am the ultimate authority of course, but as a first step, the dictionary is always best.

> Ultimately, math words means whatever standard textbokks and the mathematical community want them to mean.

Nonsense.

[markus...@gmail.com]

Of course, you are right and everyone else is wrong.

The Dunning–Kruger effect in action.

[zelos...@gmail.com]

You are not the authority on what words mean in mathematics. You are no authority in mathematics

[Eram semper recta]

The ONLY correct statement you've made in all your shit posts.

>
> The Dunning–Kruger effect in action.

An unscientific study that was conducted on 50 undergrad psychology students at one university alone and won the IgNobel awards.

Do you even actually research the bullshit that is written on Wikipedia Moronica? LMAO.

On the other hand, a scientific study conducted on cranks like you:

www.newyorker.com/magazine/2017/02/27/why-facts-dont-change-our-minds

[zelos...@gmail.com]

When you think everyone else is always wrong, and you are always right, 99% of the time, you are in fact wrong.

The studies on Dunning-kruger effect has been plenty and many and it shows up over and over again. Idiots like you overestimate your abilities significantly while knowledgable people like Marcus and I underestimate our abilities.

[Eram semper recta]

Confirmation bias is the most serious problem where mainstream math academics are concerned.

[zelos...@gmail.com]

Especially for cranks like you

[Greg Cunt]

On Tuesday, September 7, 2021 at 2:37:50 PM UTC+2, markus...@gmail.com wrote:
> >
> > Webster: too many to be counted.
> >

> What does "too many to be counted" mean?

In JG's case, more than three.

[Mostowski Collapse]

Can you do real analysis with your calculus. Lets say I want
lim x->a f(x), abstractly as an operator. But you give me

only abstractly as an operator derivative g'(x). When I have derivate
operator, can I also perform limit operation somehow by

means of the derivate operator?

[Mostowski Collapse]

Lets give it a try, what does g'(x) traditionally mean:

g(x+h) - g(x)
g'(x) = lim h->0 -------------------
h

Lets try g(x) = f(x)*(x-a), then we have:

f(a+h)*h - 0
g'(a) = lim h->0 -------------------
h

= lim h->0 f(a+h)

= lim x->a f(x)

Cool!

P.S.: The product rule is imprecise here:

(f(x)*(x-a))' = f'(x)*(x-a) + f(x)

The above only holds where f(x) is defined,
we can then plugin a, and do get:

(f(x)*(x-a))' where x=a

= f'(a)*(a-a) + f(a)

= f(a)

Where f(x) is undefined, you need the limit.

[Mostowski Collapse]

Lets do an example, what is:

sin x
lim x->0 ----- = ?
x

So we take the derivative of sin(x)/x*(x-0).
Should be the same derivative as of sin(x),
because a few singularities do not change

the derivative. And the derivative of
sin(x), is the following:

sin(x)' = cos(x)

So we have:

cos(x) where x=0 = 1

Therefore:

sin x
lim x->0 ----- = 1
x

Mostowski Collapse schrieb:

[Gale Binz]

Mostowski Collapse wrote:

> Can you do real analysis with your calculus. Lets say I want lim x->a
> f(x), abstractly as an operator. But you give me
>
> only abstractly as an operator derivative g'(x). When I have derivate
> operator, can I also perform limit operation somehow by
>
> means of the derivate operator?

Young fit healthy man gets vaxxed then goes to the gym a few days later
and has a heart attack! Kiss my dirty ass.

[Mostowski Collapse]

Is that you micro penis? What do you do in a gym?

[markus...@gmail.com]

Of course, you are right and everyone else is wrong. Everyone else is a vile Jewish homosexual mainstream infinitist.

[Eram semper recta]

Exactly. I am right and everyone else in the mainstream math community is wrong. This is FACT. I am smarter than anyone I know and yes, I do know better. This is not arrogance. It's the truth. I am a genius and the world's greatest living mathematician.

> Everyone else is a vile Jewish homosexual mainstream infinitist.

LMAO. No, just a lot of the cunts on this newsgroup.

[Quantum Bubbles]

On Wednesday, September 15, 2021 at 9:21:43 PM UTC+1, Eram semper recta wrote:

"I am smarter than anyone I know and yes, I do know better. This is not arrogance. It's the truth. I am a genius and the world's greatest living mathematician."

Oh dear, some important lessons have yet to be learned by JG 115, such as this one:

https://www.youtube.com/watch?v=n_Jbk6gqRfo

We keep hearing big talk (from JG 115) about him being a genius, but so far when asked for proof (like a Mensa test result) it always seems to be lost down the back of the sofa, or the dog ate his homework or something. Strange that. Some of us have the guts to take IQ tests, and some of us don't it seems. I wonder why....

QB

[markus...@gmail.com]

You're a genius, so much of a genius you misunderstand undergraduate mathematics.

[FromTheRafters]

Gale Binz wrote :

Yep, them gyms'll kill ya.

[zelos...@gmail.com]

it is arrogance because we can point out where you get things wrong.

[Eram semper recta]

You aren't able to point out anything, because in order to do this, you require understanding and intelligence - you have neither.

You object because it's your incorrect opinion that makes object.

[Ross A. Finlayson]

Linearization / small-angle approximation.

[zelos...@gmail.com]

I understand mathematics far better than you :)

For example a simple understanding of dedekinds cuts show that you CANNOT have finite sets as cuts! And it takes little intelligence to understand it yet you fail!

[Eram semper recta]

LMAO. You've never learned any mathematics at Oops-Allah (Uppsala) university.

>
> For example a simple understanding of dedekinds cuts show that you CANNOT have finite sets as cuts!

A simple understanding also shows that you can't have "infinite set" because there is no such thing. ROFLMAO.

> And it takes little intelligence to understand it yet you fail!

It takes even less intelligence to know you are an idiot.

[zelos...@gmail.com]

>LMAO. You've never learned any mathematics at Oops-Allah (Uppsala) university.

I learned a lot at Uppsala :)Much more than you know!

>A simple understanding also shows that you can't have "infinite set" because there is no such thing.

In ZFC you can and do have such sets so you are wrong. You have subscribed to finitism but there is nothing in mathematics that says infinite sets do not work. Infact we know axiom of infinity is independent of the rest meaning it does not add contradictions.

>It takes even less intelligence to know you are an idiot.

Yet I know more than you :)

[Alan Mackenzie]

Eram semper recta <thenewc...@gmail.com> wrote:
> On Friday, 17 September 2021 at 07:59:45 UTC+3, zelos...@gmail.com wrote:
>> torsdag 16 september 2021 kl. 07:35:20 UTC+2 skrev Eram semper recta:

[ .... ]

>> > You object because it's your incorrect opinion that makes object.
>> I understand mathematics far better than you :)

> LMAO. You've never learned any mathematics at Oops-Allah (Uppsala)
> university.

>> For example a simple understanding of dedekinds cuts show that you
>> CANNOT have finite sets as cuts!

> A simple understanding also shows that you can't have "infinite set"
> because there is no such thing. ROFLMAO.

John, you're doing it again. Remember, you don't understand what it
means for something mathematical to exist or not, therefore you're not
in any position to state infinite sets don't exist. They do, actually.

>> And it takes little intelligence to understand it yet you fail!

> It takes even less intelligence to know you are an idiot.

Oh, the erudition! ;-(

--
Alan Mackenzie (Nuremberg, Germany).

[Eram semper recta]

On Friday, 17 September 2021 at 08:40:43 UTC+3, zelos...@gmail.com wrote:
> >LMAO. You've never learned any mathematics at Oops-Allah (Uppsala) university.

> I learned a <drivel>

What you have clearly demonstrated is that you and Klyver do not understand at all what is a <factor>. How embarrassing!

A factor is any magnitude that measures (is a divisor in modern lingo) another exactly.

LMAO.

[zelos...@gmail.com]

integral domains and fields work differently. One has factor being meaningful, the other doesn't.

[Eram semper recta]

Also irrelevant. You're just trying to make your narrative seem like the right one, but the facts are clear that you are a bullshitter who knows nothing about mathematics.

To makes a statement like "integral domains and fields work differently" only shows that once again you are trying to pull the authority card. Chuckle. Poor Malum, it must be so embarrassing for you:

"h*f(x)/h means that h is a factor of f(x)" - Markus Klyver (Chambers Uni) / Zelos Malum (Uppsala)

Therefore by the "brilliant" logic of these two math master graduates, we arrive at the stunning result:

"pi*f(x)/pi means that pi is a factor of f(x)" - Markus Klyver (Chambers Uni) / Zelos Malum (Uppsala)

Tsk, tsk, tsk, tsk.

A factor is any magnitude that measures (is a divisor in modern lingo) another exactly.

This has nothing to do with your bullshit of fields, rings, etc. LMAO.

[zelos...@gmail.com]

>Clearly you have no clue what it means for a "set " to be countable.

I do, again, a set is countable if it is in bijection with a subset of N

>It has EVERYTHING to do with indexing.

No it doesn't, given an index set can be any set so it is entirely worthless.

>A set is countable IF AND ONLY IF it can be indexed. When one talks about bijection between imaginary "real sets", there is nothing about countbility there, only that one set is scaled to another. Flags do not imply equinumerosity.

Sorry to inform you but it is about bijection with subset of N, not indexing because any set, even 2^N, can be used for indexing and 2^N is not countable.

>rrelevant. You're just trying to make your narrative seem like the right one, but the facts are clear that you are a bullshitter who knows nothing about mathematics.

Very relevant. The fact is still you do not understand the difference between fields and integral domains and that is the major issue for you.

I know mathematics much better than you :) I can cite sources you can only cite your own garbage.

>To makes a statement like "integral domains and fields work differently" only shows that once again you are trying to pull the authority card. Chuckle. Poor Malum, it must be so embarrassing for you:

I pulled no authority on it. I can DEMONSTRATE they work differently based on definitions. There is no authority on it.

>Tsk, tsk, tsk, tsk.

Indeed tsk tsk tsk, you still fail to understand that integral domains and fields do work differently and factorization is only a relevant property in one of them.

[Eram semper recta]

On Monday, 6 September 2021 at 13:18:16 UTC+3, Eram semper recta wrote:
> Calculus is 100% pure geometry. What you have in mainstream calculus is the result of centuries of inability and incompetence to produce a rigorous formulation.
>

> But do not despair! I have done it:
>
> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
>
>
> Preempting anonymous coward and king troll of sci.math Dan Christensen who will no doubt spam my threads:
>
>
> > "There are no points on a line."
>
> Lie. I never said that. What I did say is that a line does not consists of points. When we talk about points on a line, we really mean distances that are indicated much like road signs do for distances travelled along a road.
>
> A line is one of innumerable distances between any two points.
> A straight line is the shortest distance between two points.
>
>
> > "Pi is NOT a number of ANY kind!"
>
> True. Pi is merely a symbol for an incommensurable magnitude - apparently a concept too advanced for an imbecile like Dan Christensen.
>
> > "1/2 not equal to 2/4"
>
> Lie. I have NEVER said this. What I have talked about is the difference in the process of measure.
> What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
> 2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.
>
> There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:
>
> _ / _ _
> _ _ / _ _ _ _
>
> The length _ is not equal to the length _ _ .
>
> > “1/3 does NOT mean 1 divided by 3 and never has meant that”
>
> True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail:
>
> https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w
>
> Also, my article on pi not being a number of any kind:
>
> https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3
>
> The true story of how we got numbers:
>
> https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU
>
> No such thing as a "real number" or a "real number line":
>
> https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc
>
> There is no valid construction of "real number" - it's a myth:
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
>
> > "3 =< 4 is nonsense.”
>
> True. In mathematics, it is called an invalid disjunction.
>
> 3 <= 4 means EITHER 3 < 4 OR 3 = 4
>
> Actually, there is no "OR" part, so the logical disjunction is invalid.
>
> > "Zero is not a number."
>
> True. While not a number of any kind, it is very useful in mathematics.
>
> https://drive.google.com/file/d/1w2tt7IgoIu-ychDCoYi-4jOAzToy0ViM
>
> > "0 is not required at all in mathematics, just like negative numbers."
>
> Half-truth. While negative numbers are not required in mathematics, they are extremely useful.
>
> > “There is no such thing as an empty set.”
>
> True. Even the father of all mainstream mathematical cranks rejected the idea of empty set. But let's not go too far ... there isn't even a definition of "set" in set theory!
>
> https://youtu.be/KvxjOMW6Q9w
>
> https://youtu.be/1CcSsOG0okg
>
> > “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
>
> True. These are propositions that are implied by the given equations. For example, my historic geometric identity states:
>
> [f(x+h)-f(x)]/h = dy/dx + Q(x,h)
>
> And so, f(x+h)-f(x)]/h <=> dy/dx + Q(x,h)
>
> The theorem:
>
> https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj
>
> How it provides a rigorous definition of integral for the flawed mainstream calculus:
>
> https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
>
> The day will come when this vicious anonymous troll Dan Christensen is convicted in a court of law.
>
> Download for free the most important mathematics book ever written:
>
> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
>
> The New Calculus is proof that you CAN DO calculus without the use of LIMIT THEORY.
>
> Don't believe me? Study it. You will be pleasantly surprised.
>
> I am a genius and the greatest mathematician alive today.

Refreshed due to troll activity.

[zelos...@gmail.com]

pointing out where you're wrong is not trolling.

[Eram semper recta]

Malum: "pi is a factor of 6 and I am only pointing out where you are wrong." LMAO

Trolls love to talk about set theory because they don't understand the OP and know that it is much easier to bullshit using set theory or topology than it is to discuss sound mathematics.

Stick to the topic please! No one is interested in your drivel.

[zelos...@gmail.com]

Why when you fail? :)

No one is trolling you. As I have pointed out, "factor" is pointless in fields, it is only in integral domains and such they are relevant.

No one is bullshitting. The issue you have with advanced math is that
1: You do not understand them worth a damn.
2: They make you look and feel as stupid as you are
3: They demonstrate all things wrong with you.
4: They are rigorous and strict so you cannot bullshit.

No one bullshits in set theory or the likes, the issue is YOU do not understand it!

You cannot understand the difference between "subset of" and "member of"

[Eram semper recta]

[zelos...@gmail.com]

It isn't trolling pointing out where you're wrong.

[Eram semper recta]

It is trolling when you confirm with your every comment that you are a troll and that's what you do. I mean even the infamous troll Dan Christensen seems to have mellowed compared to you. Now that's a poke in your eye. LMAO.

If you have nothing to say, the best practice is to abstain from taking a dump on the thread by repeating your drivel over and over again - so typical of a troll.

[Eram semper recta]

On Thursday, 23 September 2021 at 11:12:28 UTC+3, zelos...@gmail.com wrote:

[zelos...@gmail.com]

To be a troll I have to say things for the purpsoe of antagonizing people. I have no intent of antagonizing anyone. My intent is correcting you where you're wrong and boy there are many places where you are!

You repeat your drivel, so by your definition, you are a troll!

You are quite the hypocrite!

[Eram semper recta]

All we have are troll comments and nothing of substance.

[markus...@gmail.com]

Factors are defined for commutative rings.

[Eram semper recta]

Spoiler Alert: This topic is NOT about factors.

[markus...@gmail.com]

Well, you claim that factors define your function Q... so yes. I'm pointing out your definition of Q doesn't make sense.

[mitchr...@gmail.com]

we don't know the area inside a circle accurately
because we cannot measure PI to much accuracy...
it has a natural measurement limit.
If there is a formula it could never be verified
by what would be required.

Mitchell Raemsch

[Kye Fox]

nonsense. It's easy to draw a circle, the task is to find its center.