The New Calculus is being used by many mainstream academics even though they are too afraid to admit it.

Here is what one had to say about using the auxiliary equation only possible in the New Calculus:

"Haven't they accepted your calculus , how much fun is that I used your auxiliary equation of derivatives to publish some of my results in complex analytic continuation in Canada. May god give them sense , what a laugh out loud for them on one side they let me publish your results and on other side you are not getting attention."

https://www.youtube.com/watch?v=zxfUn_iAM7U

This is just one application but there are many I haven't shared. Another very useful application of the auxiliary equation is in image recognition. Nothing beats it.

If you haven't learned the New Calculus yet, now is your chance. Download my free eBook here for an introduction:

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

The free eBook is a collection of several papers that I have written over many decades. However, it is only a small part of what I have not yet shared with the public.

On Monday, July 26, 2021 at 8:58:17 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:
> The New Calculus is being used by many mainstream academics even though they are too afraid to admit it.
>

Liar. Any working mathematician, scientist or engineer can tell you that derivative of f(x)=|x| is -1 for x<0, +1 for x>0 and undefined for x=0. It is intuitively obvious from its V-shaped graph, but it causes your goofy little system to blow up. It's a boat that can't float, never mind take to the open sea, Troll Boy. For the sake of your own mental health, you really must cut your losses here and move on.

**********************************************************************************************************************
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

On Monday, July 26, 2021 at 1:58:17 PM UTC+1, Eram semper recta wrote:
> The New Calculus is being used by many mainstream academics even though they are too afraid to admit it.
>
> Here is what one had to say about using the auxiliary equation only possible in the New Calculus:
>
> "Haven't they accepted your calculus , how much fun is that I used your auxiliary equation of derivatives to publish some of my results in complex analytic continuation in Canada. May god give them sense , what a laugh out loud for them on one side they let me publish your results and on other side you are not getting attention."
>
> https://www.youtube.com/watch?v=zxfUn_iAM7U
>
> This is just one application but there are many I haven't shared. Another very useful application of the auxiliary equation is in image recognition. Nothing beats it.
>
> If you haven't learned the New Calculus yet, now is your chance. Download my free eBook here for an introduction:
>
> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
>
> The free eBook is a collection of several papers that I have written over many decades. However, it is only a small part of what I have not yet shared with the public.

Now this is a shame Mr Gabriel. If your approach really did make certain aspects of analytic continuation easier, that would not make it a replacement for calculus or analysis, but would constitute a quirky application worth noting. That would then be in addition to resembling the 16/17th century pre-limit methods in ordinary applications to analytic geometry, which I have mentioned before.

So its a shame that the channel complimenting you was setup today, has a name that translates into English as "see", and mimics some of your textual patterns. Does it keep feet warm as well?

By contrast, if you can link to the alleged published paper in question, in a peer reviewed journal, presumably you would be cited by the (alleged) correspondent?

Have a Wonderful Day
QB

Remain Calm and Keep Loving Real Analysis
[Recommended Book of the Day: When Least is Best, by Paul Nahin]

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

> Though really quite disturbing, interested readers should see:

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

On Monday, 26 July 2021 at 08:58:17 UTC-4, Eram semper recta wrote:
> The New Calculus is being used by many mainstream academics even though they are too afraid to admit it.
>
> Here is what one had to say about using the auxiliary equation only possible in the New Calculus:
>
> "Haven't they accepted your calculus , how much fun is that I used your auxiliary equation of derivatives to publish some of my results in complex analytic continuation in Canada. May god give them sense , what a laugh out loud for them on one side they let me publish your results and on other side you are not getting attention."
>
> https://www.youtube.com/watch?v=zxfUn_iAM7U
>
> This is just one application but there are many I haven't shared. Another very useful application of the auxiliary equation is in image recognition. Nothing beats it.
>
> If you haven't learned the New Calculus yet, now is your chance. Download my free eBook here for an introduction:
>
> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
>
> The free eBook is a collection of several papers that I have written over many decades. However, it is only a small part of what I have not yet shared with the public.

Students:

The Gabriel Polynomial has been used in several applications ranging from marine biology to engineering and computer science.

Study it here:

https://drive.google.com/file/d/1MnnnczqCA6vAEEoL1_OQAabDyHHzNcwW

Eram semper recta wrote:

> Students:
> The Gabriel Polynomial has been used in several applications ranging
> from marine biology to engineering and computer science.

the most stupidest, incompetent and uneducated in mathematics morons here

quantum babbles, eram rectum and dan christensen

why on earth are you sisters wasting bandwidth in a science forum??

On Monday, July 26, 2021 at 11:42:56 AM UTC-4, I am Super Rectum (aka John Gabriel) wrote...

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

> > "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.
>

Nothing "invalid" about it, Troll Boy.

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

It means 3 < 4 OR 3 = 4, which is always truly.

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.

> 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 logical proposition or 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 wrote:

> Here is what one had to say about using the auxiliary equation only
> possible in the New Calculus:

EXPOSED! - CDC RECALLS PCR Tests For FALSE POSITIVES! - Conspiracy
"Theorists" Right AGAIN!
https://www.bitchute.com/video/jxxdsZKqOLbY/

Remember, the hoax *covid-19_test_kits* made before 2017, shipped around
the world starting 2017. Made to test "positive" for common flu,
influenza A and B.

This is proof that Covid doesn’t exists, as it can’t differentiate the
flu from Covid.

On Monday, July 26, 2021 at 8:47:51 AM UTC-7, Eram semper recta wrote:
> On Monday, 26 July 2021 at 08:58:17 UTC-4, Eram semper recta wrote:
> > The New Calculus is being used by many mainstream academics even though they are too afraid to admit it.
> >
> > Here is what one had to say about using the auxiliary equation only possible in the New Calculus:
> >
> > "Haven't they accepted your calculus , how much fun is that I used your auxiliary equation of derivatives to publish some of my results in complex analytic continuation in Canada. May god give them sense , what a laugh out loud for them on one side they let me publish your results and on other side you are not getting attention."
> >
> > https://www.youtube.com/watch?v=zxfUn_iAM7U
> >
> > This is just one application but there are many I haven't shared. Another very useful application of the auxiliary equation is in image recognition. Nothing beats it.
> >
> > If you haven't learned the New Calculus yet, now is your chance. Download my free eBook here for an introduction:
> >
> > https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
> >
> > The free eBook is a collection of several papers that I have written over many decades. However, it is only a small part of what I have not yet shared with the public.
> Students:
>
> The Gabriel Polynomial has been used in several applications ranging from marine biology to engineering and computer science.
>
> Study it here:
>
> https://drive.google.com/file/d/1MnnnczqCA6vAEEoL1_OQAabDyHHzNcwW

How do you know it is right without testing it?
Don't you test its reality by the applications you suggest are being used?

Mitchell Raemsch

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

> Though really quite disturbing, interested readers should see:

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

On Tuesday, July 27, 2021 at 8:15:40 AM UTC-4, I am Super Rectum (aka John Gabriel) wrote:
> Anonymous coward...

Mr. Rectum here is at a loss for words. He can only mindlessly repeat his failed arguments. What a moron.

Dan

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

> Though really quite disturbing, interested readers should see:

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

On 7/27/2021 1:22 PM, Eram semper recta wrote:
> 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 comprised of an infinite amount of points.

Chris M. Thomasson wrote:

> On 7/27/2021 1:22 PM, Eram semper recta wrote:
>> 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 comprised of an infinite amount of points.

Not sure, longer lines provable may have more points. Curved lines may
require embedding into 2D and even 3D manifolds. Lines may be smooth or
zigzagging in sharp corners.

On Tuesday, 27 July 2021 at 16:34:46 UTC-4, Chris M. Thomasson wrote:
> On 7/27/2021 1:22 PM, Eram semper recta wrote:
> > 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 comprised of an infinite amount of points.

No. This is not true. A line's chief attribute is its distance or length. Only two points play a part in determining this length.

Points are like road signs - they are no more part of any line than the road signs are part of the road.

On 7/27/2021 1:45 PM, Walker Rodriguez-Larrinaga wrote:
> Chris M. Thomasson wrote:
>
>> On 7/27/2021 1:22 PM, Eram semper recta wrote:
>>> 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 comprised of an infinite amount of points.
>
> Not sure, longer lines provable may have more points. Curved lines may
> require embedding into 2D and even 3D manifolds. Lines may be smooth or
> zigzagging in sharp corners.
>

I can plot the same amount of points for a short line or a long line,
curves or not. It depends on the desired granularity. Fwiw, each field
line is rendered on a segment-by-segment basis:

http://fractallife247.com/test/vfield/

The segment length of an individual line can be anything one desires.
Therefore a line has an infinite number of points to play with.

For 3d, well:

https://fractalforums.org/gallery/1612-110621024937.png

https://youtu.be/BUbMJJyj7AU

On Tuesday, 27 July 2021 at 16:51:39 UTC-4, Chris M. Thomasson wrote:
> On 7/27/2021 1:45 PM, Walker Rodriguez-Larrinaga wrote:
> > Chris M. Thomasson wrote:
> >
> >> On 7/27/2021 1:22 PM, Eram semper recta wrote:
> >>> 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 comprised of an infinite amount of points.

Spoken like a true idiot that you are.

On 7/27/2021 1:52 PM, Eram semper recta wrote:
> On Tuesday, 27 July 2021 at 16:51:39 UTC-4, Chris M. Thomasson wrote:
>> On 7/27/2021 1:45 PM, Walker Rodriguez-Larrinaga wrote:
>>> Chris M. Thomasson wrote:
>>>
>>>> On 7/27/2021 1:22 PM, Eram semper recta wrote:
>>>>> 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 comprised of an infinite amount of points.
>
> Spoken like a true idiot that you are.
>

How can you disagree with me? There are an infinite number of points on
a line.

On 7/27/2021 1:51 PM, Eram semper recta wrote:
> On Tuesday, 27 July 2021 at 16:34:46 UTC-4, Chris M. Thomasson wrote:
>> On 7/27/2021 1:22 PM, Eram semper recta wrote:
>>> 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 comprised of an infinite amount of points.
>
> No. This is not true. A line's chief attribute is its distance or length. Only two points play a part in determining this length.
>
> Points are like road signs - they are no more part of any line than the road signs are part of the road.
>

A point on a line. Think about it. WOW!

On 7/26/2021 8:47 AM, Eram semper recta wrote:
> On Monday, 26 July 2021 at 08:58:17 UTC-4, Eram semper recta wrote:
>> The New Calculus is being used by many mainstream academics even though they are too afraid to admit it.
>>
>> Here is what one had to say about using the auxiliary equation only possible in the New Calculus:
>>
>> "Haven't they accepted your calculus , how much fun is that I used your auxiliary equation of derivatives to publish some of my results in complex analytic continuation in Canada. May god give them sense , what a laugh out loud for them on one side they let me publish your results and on other side you are not getting attention."
>>
>> https://www.youtube.com/watch?v=zxfUn_iAM7U
>>
>> This is just one application but there are many I haven't shared. Another very useful application of the auxiliary equation is in image recognition. Nothing beats it.
>>
>> If you haven't learned the New Calculus yet, now is your chance. Download my free eBook here for an introduction:
>>
>> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO
>>
>> The free eBook is a collection of several papers that I have written over many decades. However, it is only a small part of what I have not yet shared with the public.
>
> Students:
>
> The Gabriel Polynomial has been used in several applications ranging from marine biology to engineering and computer science.
>
> Study it here:
>
> https://drive.google.com/file/d/1MnnnczqCA6vAEEoL1_OQAabDyHHzNcwW
>

Can you use it in a Newton Fractal to help find roots?

Chris M. Thomasson wrote:

>>> A line is comprised of an infinite amount of points.
>>
>> Not sure, longer lines provable may have more points. Curved lines may
>> require embedding into 2D and even 3D manifolds. Lines may be smooth or
>> zigzagging in sharp corners.
>>
> I can plot the same amount of points for a short line or a long line,
> curves or not. It depends on the desired granularity. Fwiw, each field
> line is rendered on a segment-by-segment basis:

that's cheating. By def, a point is zero sized. Your granularity argument
is just aesthetic, as drawing arbitrary points on a blackboard or paper.
Just think, if applicable.

On 7/27/2021 2:14 PM, Walker Rodriguez-Larrinaga wrote:
> Chris M. Thomasson wrote:
>
>>>> A line is comprised of an infinite amount of points.
>>>
>>> Not sure, longer lines provable may have more points. Curved lines may
>>> require embedding into 2D and even 3D manifolds. Lines may be smooth or
>>> zigzagging in sharp corners.
>>>
>> I can plot the same amount of points for a short line or a long line,
>> curves or not. It depends on the desired granularity. Fwiw, each field
>> line is rendered on a segment-by-segment basis:
>
> that's cheating. By def, a point is zero sized. Your granularity argument
> is just aesthetic, as drawing arbitrary points on a blackboard or paper.
> Just think, if applicable.
>

Huh? A point is a location. There are an infinite number of points on a
line. Get it? Wow!

Chris M. Thomasson wrote:

> On 7/27/2021 2:14 PM, Walker Rodriguez-Larrinaga wrote:
>> Chris M. Thomasson wrote:
>>
>>>>> A line is comprised of an infinite amount of points.
>>>>
>>>> Not sure, longer lines provable may have more points. Curved lines
>>>> may require embedding into 2D and even 3D manifolds. Lines may be
>>>> smooth or zigzagging in sharp corners.
>>>>
>>> I can plot the same amount of points for a short line or a long line,
>>> curves or not. It depends on the desired granularity. Fwiw, each field
>>> line is rendered on a segment-by-segment basis:
>>
>> that's cheating. By def, a point is zero sized. Your granularity
>> argument is just aesthetic, as drawing arbitrary points on a blackboard
>> or paper. Just think, if applicable.
>
> Huh? A point is a location. There are an infinite number of points on a
> line. Get it? Wow!

you talk about granularity, fucking stupid, but points are zero sized.
What an idiot. Another one.

A point is an idealized, primitive notion. It does not have any physical
size to speak of.

A geometric (0-dimensional) point that may be assigned a finite mass.
Since a point has zero volume, the density of a point mass having a
finite mass is infinite, so point masses do not exist in reality.

On 7/27/2021 2:32 PM, Walker Rodriguez-Larrinaga wrote:
> Chris M. Thomasson wrote:
>
>> On 7/27/2021 2:14 PM, Walker Rodriguez-Larrinaga wrote:
>>> Chris M. Thomasson wrote:
>>>
>>>>>> A line is comprised of an infinite amount of points.
>>>>>
>>>>> Not sure, longer lines provable may have more points. Curved lines
>>>>> may require embedding into 2D and even 3D manifolds. Lines may be
>>>>> smooth or zigzagging in sharp corners.
>>>>>
>>>> I can plot the same amount of points for a short line or a long line,
>>>> curves or not. It depends on the desired granularity. Fwiw, each field
>>>> line is rendered on a segment-by-segment basis:
>>>
>>> that's cheating. By def, a point is zero sized. Your granularity
>>> argument is just aesthetic, as drawing arbitrary points on a blackboard
>>> or paper. Just think, if applicable.
>>
>> Huh? A point is a location. There are an infinite number of points on a
>> line. Get it? Wow!
>
> you talk about granularity, fucking stupid, but points are zero sized.
> What an idiot. Another one.

Points are locations. You seem to have some sort of mental block that
two points can define a line, and there are infinite points on that
line. WOW!

>
> A point is an idealized, primitive notion. It does not have any physical
> size to speak of.
>
> A geometric (0-dimensional) point that may be assigned a finite mass.
> Since a point has zero volume, the density of a point mass having a
> finite mass is infinite, so point masses do not exist in reality.
>

On 7/27/2021 2:32 PM, Walker Rodriguez-Larrinaga wrote:
> Chris M. Thomasson wrote:
>
>> On 7/27/2021 2:14 PM, Walker Rodriguez-Larrinaga wrote:
>>> Chris M. Thomasson wrote:
>>>
>>>>>> A line is comprised of an infinite amount of points.
>>>>>
>>>>> Not sure, longer lines provable may have more points. Curved lines
>>>>> may require embedding into 2D and even 3D manifolds. Lines may be
>>>>> smooth or zigzagging in sharp corners.
>>>>>
>>>> I can plot the same amount of points for a short line or a long line,
>>>> curves or not. It depends on the desired granularity. Fwiw, each field
>>>> line is rendered on a segment-by-segment basis:
>>>
>>> that's cheating. By def, a point is zero sized. Your granularity
>>> argument is just aesthetic, as drawing arbitrary points on a blackboard
>>> or paper. Just think, if applicable.
>>
>> Huh? A point is a location. There are an infinite number of points on a
>> line. Get it? Wow!
>
> you talk about granularity, fucking stupid, but points are zero sized.
> What an idiot. Another one.
>
> A point is an idealized, primitive notion. It does not have any physical
> size to speak of.
>
> A geometric (0-dimensional) point that may be assigned a finite mass.
> Since a point has zero volume, the density of a point mass having a
> finite mass is infinite, so point masses do not exist in reality.
>

How to draw a line with equidistant points:

void iterate_line(
ct::plot::cairo::plot_2d& plot,
glm::vec2 p0, glm::vec2 p1,
unsigned long n
){
plot.line(p0, p1, CT_RGBF(1, 1, 0));

glm::vec2 dif = p1 - p0;

float unit_base = 1. / (n - 1);

for (unsigned long i = 0; i < n; ++i)
{
float unit = unit_base * i;

glm::vec2 point = p0 + dif * unit;

plot.circle(point, .02, CT_RGBF(1, 0, 0));
}
}

unsigned long can be arbitrary in precision. n can be any natural number
greater than one. Calling iterate_line generates a line from p0 to p1
with n points and n-1 equal segments in between.

So to draw a line with, say 5 equal segments and 6 points we do:

iterate_line(plot, { -1, 0 }, { .5, .5 }, 6);

We can use this simple base to generate a fractal. And we can zoom in
forever.