Of course Euler wasn't all bad. I would even say his Elements of Al-gibberish is still by far the best text book for learning and mastering by practising of algebra, but not so much for understanding.

It's just that he made several mistakes that have been overlooked to the detriment of mathematics. S = Lim S is Euler's worst blunder. It is a stain on his legacy. Euler should not have strayed into murky waters. The consequences of his error have left a profound mark on the development of mainstream "mathematics":

https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

What is really strange, is how much attention Euler paid to Newton's fake infinite series and how he showed that any ratio can be written in one of innumerably many closed forms, but in spite of this, still maintained:

Daher ist unser Bruch 1/(1+a) gleich dieser unendlichen Reihe 1 - a + aa - aaa + ..&c

Literal translation word for word:

Therefore is our fraction 1/(1+a) EQUAL this unending series 1 - a + aa - aaa + ..&c

The series 1 - a + aa - aaa + ..&c is S. [A]
The fraction 1/(1+a) is Lim S. [B]

[A] gleich (EQUAL) [B] means S = Lim S

It's not only ignorant and stupid to deny this, but to insist that Euler thought about it in terms of limits, is dishonest and wrong.

To define two fundamentally different objects S and Lim S as equal is an unpardonable sin in mathematics.

Things equal to the same thing are equal to one another.

- Common Notion 1, Euclid's Elements

Yes, I do know better!

Your comments are drivel and shall probably be ignored.

On Friday, May 14, 2021 at 7:32:04 AM UTC-4, I am Super Rectum (aka "John Gabriel", "Troll Boy") wrote:
> S = Lim S is Euler's worst blunder. It is a stain on his legacy....

No, Troll Boy, "S = Lim S" will ALWAYS be one of SOOOOOO MANY stains on your, ahem... "legacy!" When are you going to man up and admit that it was YOU, not Euler, how wrote in big red letters, defacing a photo of his original article with your own nonsensical "S = Lim S?" You where hoping that at least some readers here were dumb as you are, right? It didn't quite work out for you did it, Troll Boy? What a moron! Time to cut your losses and move on. Math just isn't your thing.

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 Friday, 14 May 2021 at 07:32:04 UTC-4, Eram semper recta wrote:
> Of course Euler wasn't all bad. I would even say his Elements of Al-gibberish is still by far the best text book for learning and mastering by practising of algebra, but not so much for understanding.
>
> It's just that he made several mistakes that have been overlooked to the detriment of mathematics. S = Lim S is Euler's worst blunder. It is a stain on his legacy. Euler should not have strayed into murky waters. The consequences of his error have left a profound mark on the development of mainstream "mathematics":
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
>
> What is really strange, is how much attention Euler paid to Newton's fake infinite series and how he showed that any ratio can be written in one of innumerably many closed forms, but in spite of this, still maintained:
>
> Daher ist unser Bruch 1/(1+a) gleich dieser unendlichen Reihe 1 - a + aa - aaa + ..&c
>
> Literal translation word for word:
>
> Therefore is our fraction 1/(1+a) EQUAL this unending series 1 - a + aa - aaa + ..&c
>
> The series 1 - a + aa - aaa + ..&c is S. [A]
> The fraction 1/(1+a) is Lim S. [B]
>
> [A] gleich (EQUAL) [B] means S = Lim S
>
> It's not only ignorant and stupid to deny this, but to insist that Euler thought about it in terms of limits, is dishonest and wrong.
>
> To define two fundamentally different objects S and Lim S as equal is an unpardonable sin in mathematics.
>
> Things equal to the same thing are equal to one another.
>
> - Common Notion 1, Euclid's Elements
>
> Yes, I do know better!
>
> Your comments are drivel and shall probably be ignored.

It's a real shame that mainstream academics are so stupid and dishonest.

fredag 14 maj 2021 kl. 13:32:04 UTC+2 skrev Eram semper recta:
> Of course Euler wasn't all bad. I would even say his Elements of Al-gibberish is still by far the best text book for learning and mastering by practising of algebra, but not so much for understanding.
>
> It's just that he made several mistakes that have been overlooked to the detriment of mathematics. S = Lim S is Euler's worst blunder. It is a stain on his legacy. Euler should not have strayed into murky waters. The consequences of his error have left a profound mark on the development of mainstream "mathematics":
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
>
> What is really strange, is how much attention Euler paid to Newton's fake infinite series and how he showed that any ratio can be written in one of innumerably many closed forms, but in spite of this, still maintained:
>
> Daher ist unser Bruch 1/(1+a) gleich dieser unendlichen Reihe 1 - a + aa - aaa + ..&c
>
> Literal translation word for word:
>
> Therefore is our fraction 1/(1+a) EQUAL this unending series 1 - a + aa - aaa + ..&c
>
> The series 1 - a + aa - aaa + ..&c is S. [A]
> The fraction 1/(1+a) is Lim S. [B]
>
> [A] gleich (EQUAL) [B] means S = Lim S
>
> It's not only ignorant and stupid to deny this, but to insist that Euler thought about it in terms of limits, is dishonest and wrong.
>
> To define two fundamentally different objects S and Lim S as equal is an unpardonable sin in mathematics.
>
> Things equal to the same thing are equal to one another.
>
> - Common Notion 1, Euclid's Elements
>
> Yes, I do know better!
>
> Your comments are drivel and shall probably be ignored.
no one today says S=Lim S

On Monday, 17 May 2021 at 01:21:15 UTC-4, zelos...@gmail.com wrote:
> fredag 14 maj 2021 kl. 13:32:04 UTC+2 skrev Eram semper recta:
> > Of course Euler wasn't all bad. I would even say his Elements of Al-gibberish is still by far the best text book for learning and mastering by practising of algebra, but not so much for understanding.
> >
> > It's just that he made several mistakes that have been overlooked to the detriment of mathematics. S = Lim S is Euler's worst blunder. It is a stain on his legacy. Euler should not have strayed into murky waters. The consequences of his error have left a profound mark on the development of mainstream "mathematics":
> >
> > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> >
> > What is really strange, is how much attention Euler paid to Newton's fake infinite series and how he showed that any ratio can be written in one of innumerably many closed forms, but in spite of this, still maintained:
> >
> > Daher ist unser Bruch 1/(1+a) gleich dieser unendlichen Reihe 1 - a + aa - aaa + ..&c
> >
> > Literal translation word for word:
> >
> > Therefore is our fraction 1/(1+a) EQUAL this unending series 1 - a + aa - aaa + ..&c
> >
> > The series 1 - a + aa - aaa + ..&c is S. [A]
> > The fraction 1/(1+a) is Lim S. [B]
> >
> > [A] gleich (EQUAL) [B] means S = Lim S
> >
> > It's not only ignorant and stupid to deny this, but to insist that Euler thought about it in terms of limits, is dishonest and wrong.
> >
> > To define two fundamentally different objects S and Lim S as equal is an unpardonable sin in mathematics.
> >
> > Things equal to the same thing are equal to one another.
> >
> > - Common Notion 1, Euclid's Elements
> >
> > Yes, I do know better!
> >
> > Your comments are drivel and shall probably be ignored.
> no one today says S=Lim S

Fail. 0.333... = 1/3 , 0.999... = 1 and 1/7 = 0.142857... are all S = Lim S.