Dedekind and Cauchy were mainstream cranks too!

[Eram semper recta]

There is no valid construction of that mythical object called a "real number":

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

Because by definition:

A number is a name given to a measure that describes a magnitude or size.

The only true numbers are the RATIONAL NUMBERS. There are none other.

[Eram semper recta]

Gauss wrote:

"I protest against the use of an infinite quantity as something completed, which is never permissible in mathematics."

Because there is no such thing as an "infinite quantity" - it's nonsense.

[Eram semper recta]

... so protestiere ich zuvörderst gegen den Gebrauch einer unendlichen Größe als einer vollendeten, welcher in der Mathematik niemals erlaubt ist. Das Unendliche ist nur eine façon de parler, indem man eigentlich von Grenzen spricht, denen gewisse Verhältnisse so nahe kommen als man will, während anderen ohne Einschränkung zu wachsen gestattet ist. - Gauss

... so first of all I protest against the use of an infinite quantity as a completed one, which is never allowed in mathematics. The infinite is only a way of talking, in that one actually speaks of limits to which certain conditions come as close as one wants, while others are allowed to grow without restriction.


Evidently mainstream math morons pay lip service to Gauss but somehow think they know better.

The morons think not only that they can accomplish an infinite task, but they can actually perform a measure that is provably impossible, ie, 1/3 has no measure in base 10.

[Python]

Crank John Gabriel, aka Eram semper recta wrote:
>
> There is no valid construction of that mythical object called a "real number":

There are. You just fail understanding them. EOS. We are not
responsible for your deficiencies John. And we do not care, you
will die (soon) as idiot as you've always been.

[Dan Christensen]

On Sunday, August 8, 2021 at 8:48:33 PM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:
> There is no valid construction of that mythical object called a "real number":
>

Liar. There are at least two valid constructions of the reals: Dedekind cuts and equivalence classes of Cauchy sequences.

>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>

A thoroughly useless definition when it comes to actually proving things about numbers, Mr. Rectum. You are unable to even prove that 2+2=4 in your goofy little system. You, the self-styled "Greatest Mathematician Eve????" HA, HA, HA!!!!

STUDENTS BEWARE: Don't be 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!

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

[zelos...@gmail.com]

>There is no valid construction of that mythical object called a "real number"

There are, you failed to present anything that makes them invalid. All you presented was "Does not fit my ideas" which does not invalidate them.

>Because by definition

YOUR definition and YOUR idea and NOTHING else.

[New Age Prophet]

On Sunday, 8 August 2021 at 21:36:49 UTC-4, Psychopath Jean Pierre Messager aka YBM aka JPM aka Python wrote:
> >
> > There is no valid construction of that mythical object called a "real number":
> There are.

If wishes were horses, then beggars would ride.

> You just fail understanding them. EOS.

It's true, my brain is naturally vaccinated so as to protect me from garbage. My bullshit detector is better than anyone else I know.

> We are not responsible for our deficiencies John.

You will be! :)

> And we do not care, you will die (soon)...

Well, the fate of all humans is the same, but if you survive me, you will care! Chuckle.

So what about those "student projects" of yours, Jean? Were you just imagining things back then? I am still waiting to read these... I guess you were lying as you normally do.

[Dan Christensen]

On Monday, August 9, 2021 at 9:02:01 AM UTC-4, (aka John Gabriel, Troll Boy, I am Super Rectum) wrote:

> > > There is no valid construction of that mythical object called a "real number":

> > Liar. There are at least two valid constructions of the reals: Dedekind cuts and equivalence classes of Cauchy sequences.

> If wishes were horses, then beggars would ride...

And Troll Boy, Beggar of Math here, WISHES he could get his goofy little system to work. He WISHES he could determine the derivative of f(x)=|x|. He WISHES he could even prove that 2+2=4. Alas, it is not to be. He goofy little system is a boat that won't float, never mind make to the open sea. It is DOA. MIA. A twisted, smoldering wreckage in the desert of broken of dreams. Poor 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

[zelos...@gmail.com]

New account john?

[Eram semper recta]

On Monday, 9 August 2021 at 01:06:13 UTC-4, zelos...@gmail.com wrote:
> >There is no valid construction of that mythical object called a "real number"
> There are, you failed to present anything that makes them invalid. All you presented was "Does not fit my ideas" which does not invalidate them.

That is the "picture" you and your fellow cranks try to paint, but it is obviously transparent to all.

[Dan Christensen]

It is much more transparent than your goofy little system, Mr. Rectum. Unlike your goofy little system, it actually works. Deal with it.

Dan

[Timothy Golden]

Just looked for Cauchy in English and only finding the French original of Oeuvres Completes
https://archive.org/search.php?query=creator%3A%28cauchy%29&and[]=languageSorter%3A%22English%22

Anybody got a link?
Is this the work that competes with Dedekind?

[zelos...@gmail.com]

That is how it is, I can demonstrate it openly again if you want.

[Eram semper recta]

Straw man arguments, false beliefs, authoritative orders and void assertions do not constitute any kind of demonstration.

[Dan Christensen]

On Wednesday, August 11, 2021 at 8:38:44 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

> Straw man arguments, false beliefs, authoritative orders and void assertions do not constitute any kind of demonstration.

Your stock-in-trade, eh, Troll Boy?

STUDENTS BEWARE: Don't be 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!

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

[zelos...@gmail.com]

I can demonstrate it as I always have, nothing false, no straw man.

It is demonstrable, want me to?

[Eram semper recta]

Anonymous coward and king troll of sci.math Dan Christensen spammed:

> "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

[New Age Prophet]

On Sunday, August 8, 2021 at 8:48:33 PM UTC-4, Eram semper recta wrote:

Not even the gods can measure those incommensurable magnitudes denoted by π and √2, etc.

But mere mortals want to punish the gods. LMAO.

[Timothy Golden]

Here is a neat price tag to the English version, whose price as I read this link is USD760.74...
He may be good, but I doubt he is that good.
Strange that the French version is free yet no English version is free.
To make matters worse there are apparently 26 volumes: https://www.amazon.com/Oeuvres-compl%C3%A8tes-Cambridge-Library-Collection/dp/1108003176/ref=sr_1_135?dchild=1&qid=1628768686&refinements=p_27%3AAugustin-Louis+Cauchy&s=books&sr=1-135&text=Augustin-Louis+Cauchy

To think that such works so carefully published could go inaccessible...
Lots of good journals are when nobody can read them.
The quintessential exclusive medium.
Exclusivity is tantamount to racism.
Beyond that there is a problem, informationally speaking.
Does this system really add up?
When his name is mentioned as much as it is, yet his work is incommunicato it is as if he is in jail, no?
Is this in perpetuity?

[Eram semper recta]

On Thursday, 12 August 2021 at 07:59:45 UTC-4, timba...@gmail.com wrote:
> On Tuesday, August 10, 2021 at 11:38:45 AM UTC-4, Timothy Golden wrote:
> > On Sunday, August 8, 2021 at 8:48:33 PM UTC-4, Eram semper recta wrote:
> > > There is no valid construction of that mythical object called a "real number":
> > >
> > > https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
> > >
> > > Because by definition:
> > >
> > > A number is a name given to a measure that describes a magnitude or size.
> > >
> > > The only true numbers are the RATIONAL NUMBERS. There are none other.
> > Just looked for Cauchy in English and only finding the French original of Oeuvres Completes
> > https://archive.org/search.php?query=creator%3A%28cauchy%29&and[]=languageSorter%3A%22English%22
> >
> > Anybody got a link?
> > Is this the work that competes with Dedekind?
> Here is a neat price tag to the English version, whose price as I read this link is USD760.74...
> He may be good, but I doubt he is that good.
> Strange that the French version is free yet no English version is free.
> To make matters worse there are apparently 26 volumes: https://www.amazon.com/Oeuvres-compl%C3%A8tes-Cambridge-Library-Collection/dp/1108003176/ref=sr_1_135?dchild=1&qid=1628768686&refinements=p_27%3AAugustin-Louis+Cauchy&s=books&sr=1-135&text=Augustin-Louis+Cauchy
>
> To think that such works so carefully published could go inaccessible...
> Lots of good journals are when nobody can read them.

Journals are no longer relevant. Those whose drivel is published in journals are in line with the mainstream, in other words useless.

[Timothy Golden]

https://www.matharticles.com/ma/ma002.pdf

[Eram semper recta]

That is a very good link Timothy! The first paragraph is so entertaining!

Student: The car has a speed of 50 miles an hour. What does that mean?
Teacher: Given any epsilon > 0 there exists a delta > 0 such that if |t_2 - t_1| < delta then
| (s_2 - s_1)/(t_2 - t_1) - 50 | < epsilon

Student: How in the world did anybody ever think of such an answer?

LMAO. It's probably the kind of answer and idiot like Malum or his sidekick Markus Klyver would give.

The Great John Gabriel responds:

This is the typical bullshit that supposedly added rigour to calculus. Anyone with even a modicum of intelligence can know instantly that it took moronic mainstream academics over 200 years and they still FAILED to explain why calculus works or add any rigour whatsoever.

The answer is simple: Speed is a measure of how fast or slow an object moves.

Speed is understood to be the "total distance covered" measured by "time". YES morons! This is what speed means. In this example, you need 1 hour to measure every 50 miles.

[markus...@gmail.com]

That definition only works for constant speeds.

[Eram semper recta]

Nope. It works for ALL speeds. There is never a case when time (itself a distance based on constant motion of the earth. 1 s approx. equal 460 metres) does not measure distance.

[markus...@gmail.com]

What if the speed changes then?

[Eram semper recta]

Not sure what you mean? You need constant motion (speed) in order to have time. The slight changes in the earth's speed are the reason for the anomalies noticed by Einstein, not his bullshit of relativity or the absolute garbage he called space-time, etc.

[Timothy Golden]

If the speed is unknown it is not as if the theory is going to determine the speed by magic.
The idea that we are in control of the conditions of the gedanken is a dubious assumption.
Especially at the microscopic level, which is the level we must go to for higher precision.
Ultimately specifying the exact velocity of Musk's falcon heavy can only be done to some reference position
while the actual sensors deriving the value have no interaction with that reference position.
OK, possibly a constant carrier frequency could be used, but even then some delay will be entered.
The answer is that it is extremely complicated, and that accelerometers will be used to compute the current trajectory and thus the current position, even if just as a double check against the amount of fuel burned or some such other metric.

The idea that in reality epsilon delta (ed) is doing quite well; all the while chasing down to the finest digit we can... physics does reach a bottom digit; a halt and return sort of stage. Doing the math of 1/3 in radix 10 you can just keep on going, but it is the same procedure that ed used. Ed got used for zz=2 as well and if only Dedekind would have done the computation by actual instantiation we'd witness this. He claimed that this is proof of the continuum, yet as I see it this is rhetoric. He simply gave a very convincing argument that the math folk could rest upon as full and copious, and the mechanism of the cut may actually ring quite empty while ed wins the day, the week, the month, the year, and the milenium.

[markus...@gmail.com]

Apart from you butchering physics, the definition that speed is "distance covered per time" only works if the speed is constant.

[Eram semper recta]

Nonsense. The is the definition for ALL speed. The speed at an instant (slope of tangent line if a position function exists) also is parallel to many other secant lines with the same slope.

[markus...@gmail.com]

It clearly doesn't. If the speed is not constant, you need to take a limit.

[Eram semper recta]

You can't take a limit if you don't have a smooth function, you idiot!!

Calculus is both null and void without a smooth function.

[konyberg]

There are at least two definitions of speed. One is average speed: v = s/t.
And another is momentary speed: v = lim(t->0)delta(s)/delta(t).
A car doesn't know the average speed you will use from a point A to B, but it knows your momentary speed. This shows in your face.
KON

[New Age Prophet]

That is the only definition of speed.

> And another is momentary speed: v = lim(t->0)delta(s)/delta(t).

Garbage concept.

momentary speed: speed that is momentary lasts for a very short period of time.

That's the same as average speed.

> A car doesn't know the average speed you will use from a point A to B, but it knows your momentary speed. This shows in your face.

No. It knows your speed through an analog speed measuring device - has NOTHING to do with calculus.

Car speedometers usually work by measuring rotation of the car's driveshaft, axle or wheel.

> KON

[markus...@gmail.com]

That's just false. You don't need smoothness for f' to exist. Or do you have an other definition 99% of mathematicians don't use?

[markus...@gmail.com]

Both of these are the same for constant speeds.

[Eram semper recta]

It's 100% TRUE.

> You don't need smoothness for f' to exist.

You ABSOLUTELY do! I mean, even your bullshit derivative definition f'(x)=lim_{h->0} [f(x+h)-f(x)]/h assumes smoothness of f.

The finite difference quotients [f(x+h_1)-f(x)]/h_1 ; [f(x+h_2)-f(x)]/h_2 ; ... ; [f(x+h_i)-f(x)]/h_i are fucking meaningless if f is not smooth.

> Or do you have an other definition 99% of mythmaticians don't use?

Yes. It's called the New Calculus. You should try and study it some time instead of wasting your time with fellow idiots on Reddit? LMAO.

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

[markus...@gmail.com]

You don't need smoothness for f' to exist. Define f by f(x)=-x^3 for x<1 and f(x)=x^2−5x+3 otherwise. Then f is C^1 but not smooth.

[Ross A. Finlayson]

On Saturday, August 28, 2021 at 8:37:57 AM UTC-7, markus...@gmail.com wrote:
> You don't need smoothness for f' to exist. Define f by f(x)=-x^3 for x<1 and f(x)=x^2−5x+3 otherwise. Then f is C^1 but not smooth.

Continuous functions have come a long way in definition
since the only continuous functions, were effectively sinusoidal.
(And had no undefined kinks with respect to being smooth.)

Dirac's and Heaviside's or delta and step, for including those as
continuous, is that Heaviside's is the clearest step continuity while
Dirac's is instead "the infinite height unit impulse at the origin,
the area under which equals one while width is zero".
(Or as modeled by real functions.)

[Eram semper recta]

You most absolutely DO NEED smoothness. Calculus is both null and void unless a given function is smooth.

> Define f by f(x)=-x^3 for x<1 and f(x)=x^2−5x+3 otherwise.

This is your typical "piece-wise" function bullshit. -x^3 =/= x^2−5x+3 so how can you call them both f, you stupid?

Calculus methods will work on the separate functions and obviously fail at x=3 because then the function is no longer the same.

> Then f is C^1 but not smooth.

I don't subscribe to C^1 shit.

[markus...@gmail.com]

> Calculus methods will work on the separate functions and obviously fail at x=3 because then the function is no longer the same.
> > Then f is C^1 but not smooth.
> I don't subscribe to C^1 shit.

Then what do you mean by smooth? The definition 99% of all mathematicians use if that derivatives of all orders exist. The function I gave you will not have derivatives of all orders.

And of course f is a valid function: every x gives on y-value.

You can plot it in Python if you like to:

from matplotlib import pyplot as plt
import numpy as np

def fun(x):
if x<1:
return -pow(x, 3)
else:
return pow(x, 2)-5*x+3

f=np.frompyfunc(f, 1, 1)
x=np.arange(-10, 10, 0.01)
y=f(x)

plt.plot(x,y)
plt.show()

f is equal to both -x^3 and x^2−5x+3, but on different intervals.

[Eram semper recta]

On Saturday, 28 August 2021 at 16:15:22 UTC-4, markus...@gmail.com wrote:
> > Calculus methods will work on the separate functions and obviously fail at x=3 because then the function is no longer the same.
> > > Then f is C^1 but not smooth.
> > I don't subscribe to C^1 shit.
> Then what do you mean by smooth?

Geometrically, a function f is said to be smooth over an interval (a,b) if at any point in (a,b), it is the case that only ONE tangent line can be constructed. It is the tangent line that determines smoothness of any function.

> The function I gave you will not have derivatives of all orders.

It's not one function but two and since you did not answer my question, I stop responding at this point. You're a troll and an idiot.

<Drivel>

[markus...@gmail.com]

Okay, so your smoothness is simply f' existing at every point?

It is one function because every x gives an unique value y=f(x). That's the definition of a function, Gabriel.

[Eram semper recta]

On Sunday, 29 August 2021 at 09:59:14 UTC-4, markus...@gmail.com wrote:
> söndag 29 augusti 2021 kl. 02:27:58 UTC+2 skrev Eram semper recta:
> > On Saturday, 28 August 2021 at 16:15:22 UTC-4, markus...@gmail.com wrote:
> > > > Calculus methods will work on the separate functions and obviously fail at x=3 because then the function is no longer the same.
> > > > > Then f is C^1 but not smooth.
> > > > I don't subscribe to C^1 shit.
> > > Then what do you mean by smooth?
> > Geometrically, a function f is said to be smooth over an interval (a,b) if at any point in (a,b), it is the case that only ONE tangent line can be constructed. It is the tangent line that determines smoothness of any function.
> > > The function I gave you will not have derivatives of all orders.
> > It's not one function but two and since you did not answer my question, I stop responding at this point. You're a troll and an idiot.
> >
> > <Drivel>
> Okay, so your smoothness is simply f' existing at every point?

No, you fucking idiot, NO!

Go back and read my answer which tells you what smoothness means.

This discussion is also over.

[markus...@gmail.com]

Your condition means that f' should be well-defined for all x.

[zelos...@gmail.com]

What we have here is once again demonstrating you do not understand mathematics, how functions work or anything.

[Eram semper recta]

No. It means f must be defined for all x in a given interval over which f is SMOOTH.

[markus...@gmail.com]

You definition of smoothness is that f' exists (what you call the tangent line).

[Eram semper recta]

Nonsense. Of course f (not f' as you write in your drivel) must exist and the SMOOTHNESS of f is determined as I stated:

f is smooth over an interval (a,b) iff it is possible to construct no more than ONE tangent line at each point in the interval. Inflection points are excluded because no tangent line is possible at inflection points and it's no problem at all because it doesn't affect the mean value theorem or the fundamental theorem of calculus.

[zelos...@gmail.com]

Cranks who contradict some mainstream opinion in some highly technical field, (e.g. mathematics, cryptography, physics) may:

exhibit a marked lack of technical ability,
misunderstand or not use standard notation and terminology,
ignore fine distinctions which are essential to correctly understand mainstream belief.

Good example of you doing this, where you do not understand standard terminology, what smooth means.

[Eram semper recta]

All the above apply to YOU!

>
> Good example of you doing this, where you do not understand standard terminology, what smooth means.

Chuckle. You mean like the "understanding" which you demonstrate here:

"IF f=g+c THEN g=f-c is CIRCULAR" - Zelos Malum and Jean Pierre Messager (aka Python)

LMAO.

[zelos...@gmail.com]

None of thsoe fits because I understand standard notation and words, unlike you.

>Lying again, crank? Nowhere did I say this. Provide the link, you vile bastard!

https://groups.google.com/g/sci.math/c/5NjpX0It60I/m/nLvlglEMCQAJ
https://groups.google.com/g/sci.math/c/bxHjnK8_00o/m/L5t27UkMCQAJ
https://groups.google.com/g/sci.math/c/QMhqLZH1434/m/a_ShbscMCQAJ
Right in this post :slight_smile:

>I have NEVER defined the derivative in terms of a limit.

I didn't say you did, I said I did. D was defiend in terms of limit, T in terms of D, and you cry circular which is not it.

To be circular T is defined in terms of D, and D in terms of T, but it isn't. D is defined independently of T

>That's EXACTLY what YOU do in your bullshit MAINSTREAM calculus and it is CIRCULAR.

See, right here you do claim it is circular just like I said you do.

D defined in terms of limit
T defined in terms of D
Is not circular. It is a linear progression of definitions.

>Your drivel was nothing of the sort. You imagined that you were agreeing with your fellow asswipe Jean Pierre Messager (aka Python) and I made a fool of you yet again! LMAO.

You didn't, you did however manage to confirm in this post exactly what I said you did while denying it. That is quite foolish.

[Eram semper recta]

On Sunday, 8 August 2021 at 20:48:33 UTC-4, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

Essentially what the Baboons of mainstream academia will have you believe is that:

t(c+h)-t(c)]/h = Lim (h->0)[f(c+h)-f(c)]/h = f'(c) + Q(c,h) and is possible ONLY if Q(c,h)=0, but this happens only in the case of the straight line t(x). It NEVER happens with the finite difference quotients. The mainstream want you to believe that there is some finite difference ratio hovering at infinity which produces f'(c):

t(c+h)-t(c)]/h = [f(c+h_1)-f(c)]/h_1 ; [f(c+h_2)-f(c)]/h_2 ; [f(c+h_3)-f(c)]/h_3 ; ... ; [f(c+h_3n-f(c)]/h_n ...; [f(c+h_oo)-f(c)]/h_oo

t(c+h)-t(c)]/h = [f(c+h_oo)-f(c)]/h_oo ?! What?!!! There is no such finite difference. It does not exist! But Baboon mathematics of the mainstream insists there is a limit!

Can you imagine how embarrassed Newton and Leibniz would be at these idiots today?! They knew that they could not solve the tangent line problem - this had to wait for the great John Gabriel. It is I who revealed to the entire world that:

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

It usually takes a genius to realise the most simple concepts that escape the syphilitic brains of highly educated idiots in the mainstream.

[Mostowski Collapse]

If you dont know limit, consult YT:

f(x) is not calculated at a, when lim x->a f(x) = b
lim is a game!
My move is epsilon, your move is some delta.

CalcGREEN 1 : Ch. 7.1 : Limit Intuition & Definition
https://www.youtube.com/watch?v=7dYJ-DvDVf0

Prof G spot of calculus! LoL

[markus...@gmail.com]

So your criticism isn't that of f, it is that of limits. I would suggest you learning limits.

[Eram semper recta]

On Monday, 9 August 2021 at 03:48:33 UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

Nothing worth respond to here.

[Hardy Kuhn]

Eram semper recta wrote:

>> Because by definition: A number is a name given to a measure that
>> describes a magnitude or size.
>> The only true numbers are the RATIONAL NUMBERS. There are none other.
>
> Nothing worth respond to here.

How is anyone still buying this bullshit?
https://153news.net/watch_video.php?v=ADGUG4M3635H

[zelos...@gmail.com]

yet you cannot explain how mainstream is circular when you're just as circular. You cannot have tangent without derivative so you cannot use the tangent to define derivative!

[Eram semper recta]

On Monday, 9 August 2021 at 03:48:33 UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

Still nothing worthy of a response.

[zelos...@gmail.com]

Your definitions are circular :)

[Eram semper recta]

On Monday, 9 August 2021 at 03:48:33 UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

Master "math" graduates Markus Klyver (Chambers uni) and Zelos Malum (Uppsala) claim that pi is a factor of 6. Eyes rolling.

pi does not divide 6 without remainder, therefore pi IS NOT a factor of 6. How embarrassing!!! Tsk, tsk.

If this is what a master degree from Chambers and Uppsala gets you, then I urge you young Swedes to avoid both these universities. I mean, for crying out loud, neither of these fools understands what it means for a magnitude to be a <<factor>>.

[zelos...@gmail.com]

We are pointing out that your claims about factors in a field is idiotic.

[Ike Dow]

Eram semper recta wrote:

>> The only true numbers are the RATIONAL NUMBERS. There are none other.
>
> Master "math" graduates Markus Klyver (Chambers uni) and Zelos Malum
> (Uppsala) claim that pi is a factor of 6. Eyes rolling.
> pi does not divide 6 without remainder, therefore pi IS NOT a factor of
> 6. How embarrassing!!! Tsk, tsk.

the vaccine protected need to be protected form the unprotected by
forcing the unprotected to use the protection that didn't protect the
protected.

[Eram semper recta]

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, 9 August 2021 at 03:48:33 UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

Neither Dedekind, nor Cauchy, nor anyone else has ever managed to produce a valid construction of "real number".

[zelos...@gmail.com]

They have, again your supposed "cuts" are not cuts because they are finite so your complaints there are invalid.

[Eram semper recta]

On Monday, 9 August 2021 at 03:48:33 UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

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.

[NewAge Prophet]

On Monday, August 9, 2021 at 3:48:33 AM UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

Refreshed due to troll activity.

[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.

[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]

On Monday, 9 August 2021 at 03:48:33 UTC+3, Eram semper recta wrote:
> There is no valid construction of that mythical object called a "real number":
>
> https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU
>
> Because by definition:
>
> A number is a name given to a measure that describes a magnitude or size.
>
> The only true numbers are the RATIONAL NUMBERS. There are none other.

All we have are troll comments and nothing of substance.

[markus...@gmail.com]

It has everything to do with rings: a factor is an algebraic concept valid for any (commutative) ring. Some ring element b is a factor of some ring element a iff a=c*b. What makes factorisations of integers and polynomials more interesting is that they are not fields.

Anyway, you function Q remains ill-defined.

[Eram semper recta]

Spoiler alert: This topic is not about factors or whatever you mean by "Q".