Euler's vomit

Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}

is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.

More here:

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

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

Degradation is very similar to a sequence 0.9, 0.99, 0.999, etc..
What gets smaller and smaller is the difference to 1, which is:

0.1, 0.01, 0.001, etc..

No wonder John Gabriel doesn't understand mRNA degradation,
he even doesn't understand 0.999... = 1.

Possibly a brain damage or something, that he lacks any
understanding of degradation.

LMAO!

Eram semper recta schrieb am Sonntag, 8. August 2021 um 14:01:09 UTC+2:
> Euler's vomit
>
> Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
>
> is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
>
> More here:
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

On Sunday, 8 August 2021 at 08:03:45 UTC-4, Swiss moron Jan Burse aka Mostowski Collapse wrote:
> Degradation is very similar to a sequence 0.9, 0.99, 0.999, etc..
> What gets smaller and smaller is the difference to 1, which is:
>
> 0.1, 0.01, 0.001, etc..

From your very own Abel Prize winner!

"Don't trust Wackopedia."

https://youtu.be/1WepO8tFGto?t=103

LMAO

>
> LMAO!
> Eram semper recta schrieb am Sonntag, 8. August 2021 um 14:01:09 UTC+2:
> > Euler's vomit
> >
> > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> >
> > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> >
> > More here:
> >
> > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

I didn't know that Euler wrote for wikipedia.

Bird brain John Gabriel currently having a paranoid breakdown.

LMAO!

Eram semper recta schrieb am Sonntag, 8. August 2021 um 14:12:01 UTC+2:
> On Sunday, 8 August 2021 at 08:03:45 UTC-4, Swiss moron Jan Burse aka Mostowski Collapse wrote:
> > Degradation is very similar to a sequence 0.9, 0.99, 0.999, etc..
> > What gets smaller and smaller is the difference to 1, which is:
> >
> > 0.1, 0.01, 0.001, etc..
> From your very own Abel Prize winner!
>
> "Don't trust Wackopedia."
>
> https://youtu.be/1WepO8tFGto?t=103
>
> LMAO
> >
> > LMAO!
> > Eram semper recta schrieb am Sonntag, 8. August 2021 um 14:01:09 UTC+2:
> > > Euler's vomit
> > >
> > > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> > >
> > > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> > >
> > > More here:
> > >
> > > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

On Sunday, 8 August 2021 at 08:03:45 UTC-4, Shithead Jan Burse aka Mostowski Collapse wrote:

From your very own Abel Prize winner!

"Don't trust Wackopedia."

https://youtu.be/1WepO8tFGto?t=103

Wackopedia says 1 and 0.999... are equal. Hmm, I think Uhlenbeck disagrees with you! MOOOOOROOOOOON.

LMAO

Hey Burse, you've been away for a long time. Did you get fired from your cheese factory job, so you've got nothing but time on your hands to spew shit out on my threads, eh moron?

On Sunday, 8 August 2021 at 08:15:23 UTC-4, Eram semper recta wrote:
> On Sunday, 8 August 2021 at 08:03:45 UTC-4, Shithead Jan Burse aka Mostowski Collapse wrote:
>
>
> From your very own Abel Prize winner!
>
> "Don't trust Wackopedia."
>
> https://youtu.be/1WepO8tFGto?t=103
> Wackopedia says 1 and 0.999... are equal. Hmm, I think Uhlenbeck disagrees with you! MOOOOOROOOOOON.
>
> LMAO
>
> Hey Burse, you've been away for a long time. Did you get fired from your cheese factory job, so you've got nothing but time on your hands to spew shit out on my threads, eh moron?

It's bad enough that anon troll Dan Christensen relieves himself on every one of my threads. Don't you have toilets in Switzerland?

You are fooling yourself, if you blindly trust Wikipedia.
Every Wikipedia has a list of references, where they stole
the text from, copy pasta basically.

So you can check the references, and of course you
can use other sources. Nobody works with Wikipedia
per se. You never see me citing Wikipedia as a proof

of something. But I am pretty sure you can lookup the
mRNA stuff else where, Wikipedia is a good summary to
start with. Thats all. No reason to get paranoid.

You are fooling yourself, if you blindly trust Wikipedia,
or think 0.999... = 1 has anything to do with Wikipedia.

Dang, you are stupid John Gabriel, grow up.

Mostowski Collapse schrieb am Sonntag, 8. August 2021 um 14:13:47 UTC+2:
> I didn't know that Euler wrote for wikipedia.
>
> Bird brain John Gabriel currently having a paranoid breakdown.
>
> LMAO!
> Eram semper recta schrieb am Sonntag, 8. August 2021 um 14:12:01 UTC+2:
> > On Sunday, 8 August 2021 at 08:03:45 UTC-4, Swiss moron Jan Burse aka Mostowski Collapse wrote:
> > > Degradation is very similar to a sequence 0.9, 0.99, 0.999, etc..
> > > What gets smaller and smaller is the difference to 1, which is:
> > >
> > > 0.1, 0.01, 0.001, etc..
> > From your very own Abel Prize winner!
> >
> > "Don't trust Wackopedia."
> >
> > https://youtu.be/1WepO8tFGto?t=103
> >
> > LMAO
> > >
> > > LMAO!
> > > Eram semper recta schrieb am Sonntag, 8. August 2021 um 14:01:09 UTC+2:
> > > > Euler's vomit
> > > >
> > > > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> > > >
> > > > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> > > >
> > > > More here:
> > > >
> > > > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

On Sunday, 8 August 2021 at 08:01:09 UTC-4, Eram semper recta wrote:
> Euler's vomit
>
> Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
>
> is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
>
> More here:
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

It's crystal clear to any sane mind that 1/3 has no measure in base 10 and moreover that equating the series 0.333... with its limit is buffoonery. The most important number theorem tells us this fact:

https://drive.google.com/file/d/1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH

On Sunday, August 8, 2021 at 8:01:09 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:
> Euler's vomit

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 Sunday, 8 August 2021 at 10:17:59 UTC-4, Eram semper recta wrote:
> On Sunday, 8 August 2021 at 08:01:09 UTC-4, Eram semper recta wrote:
> > Euler's vomit
> >
> > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> >
> > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> >
> > More here:
> >
> > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> It's crystal clear to any sane mind that 1/3 has no measure in base 10 and moreover that equating the series 0.333... with its limit is buffoonery. The most important number theorem tells us this fact:
>
> https://drive.google.com/file/d/1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH

Poor idiot Euler.

First he says:

[22] It may be observed that no infinite series is in reality equal to the fraction from which it is derived; unless the REMAINDER be considered, which, in the present case, is alternately +1/2 and –1/2; that is, +1/2 when the series is 0, and +1/2 when the series is 1, which still gives the same value for the whole expression. Vid. Article 293.

And then this:

524. Let there now be given the infinite progression, 9+9/10+9/100+9/1000+9/10000+⋯
The first term is 9, and the ratio is 1/10. So that 1 minus the ratio is 9/10; and 9/9/10=10, the sum required: which series is expressed by a decimal fraction, thus, 9.9999999, etc.

I guess he forgot about the remainder in the one above? LMAO.

81. We can never therefore arrive completely at 0, or nothing, however great the denominator may be; and, consequently, as those fractions must always preserve a certain quantity, we may continue the series of fractions in the 78th article without interruption. This circumstance has introduced the expression that the denominator must be infinite, or infinitely great, in order that the fraction may be reduced to 0, or to nothing; hence the word infinite in reality signifies here that we can never arrive at the end of the series of the above-mentioned fraction.

Only a syphilitic brain can use expressions such as "denominator must be infinite", "infinitely great", etc.

82. To express this idea, according to the sense of it above-mentioned, we make use of the sign ∞, which consequently indicates a number infinitely great; and we may therefore say that this fraction 1/∞ is in reality nothing; because a fraction cannot be reduced to nothing, until the denominator has been increased to infinity.

∞ NEVER indicates a number, but there was no one intelligent enough to point this out to the moron Euler. There is no fraction of the form "1/∞ " because ∞ is NOT a number and only numbers can appear in the numerator and denominator of a fraction. What was the poor birdbrain Euler thinking?!

83. It is the more necessary to pay attention to this idea of infinity, as it is derived from the first elements of our knowledge, and as it will be of the greatest importance in the following part of this treatise.

Indeed! The biggest BLUNDER ever being S = Lim S.

Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}

Did you find these jokes in your shit pants?
Maybe change your diapers once a while.

Eram semper recta schrieb:
> On Sunday, 8 August 2021 at 10:17:59 UTC-4, Eram semper recta wrote:
>> On Sunday, 8 August 2021 at 08:01:09 UTC-4, Eram semper recta wrote:
>>> Euler's vomit
>>>
>>> Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
>>>
>>> is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
>>>
>>> More here:
>>>
>>> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
>> It's crystal clear to any sane mind that 1/3 has no measure in base 10 and moreover that equating the series 0.333... with its limit is buffoonery. The most important number theorem tells us this fact:
>>
>> https://drive.google.com/file/d/1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH
>
> Poor idiot Euler.
>
> First he says:
>
> [22] It may be observed that no infinite series is in reality equal to the fraction from which it is derived; unless the REMAINDER be considered, which, in the present case, is alternately +1/2 and –1/2; that is, +1/2 when the series is 0, and +1/2 when the series is 1, which still gives the same value for the whole expression. Vid. Article 293.
>
> And then this:
>
> 524. Let there now be given the infinite progression, 9+9/10+9/100+9/1000+9/10000+⋯
> The first term is 9, and the ratio is 1/10. So that 1 minus the ratio is 9/10; and 9/9/10=10, the sum required: which series is expressed by a decimal fraction, thus, 9.9999999, etc.
>
> I guess he forgot about the remainder in the one above? LMAO.
>
> 81. We can never therefore arrive completely at 0, or nothing, however great the denominator may be; and, consequently, as those fractions must always preserve a certain quantity, we may continue the series of fractions in the 78th article without interruption. This circumstance has introduced the expression that the denominator must be infinite, or infinitely great, in order that the fraction may be reduced to 0, or to nothing; hence the word infinite in reality signifies here that we can never arrive at the end of the series of the above-mentioned fraction.
>
> Only a syphilitic brain can use expressions such as "denominator must be infinite", "infinitely great", etc.
>
> 82. To express this idea, according to the sense of it above-mentioned, we make use of the sign ∞, which consequently indicates a number infinitely great; and we may therefore say that this fraction 1/∞ is in reality nothing; because a fraction cannot be reduced to nothing, until the denominator has been increased to infinity.
>
> ∞ NEVER indicates a number, but there was no one intelligent enough to point this out to the moron Euler. There is no fraction of the form "1/∞ " because ∞ is NOT a number and only numbers can appear in the numerator and denominator of a fraction. What was the poor birdbrain Euler thinking?!
>
> 83. It is the more necessary to pay attention to this idea of infinity, as it is derived from the first elements of our knowledge, and as it will be of the greatest importance in the following part of this treatise.
>
> Indeed! The biggest BLUNDER ever being S = Lim S.
>
> Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
>

On Sunday, August 8, 2021 at 12:12:43 PM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

> > It's crystal clear to any sane mind that 1/3 has no measure in base 10 and moreover that equating the series 0.333... with its limit is buffoonery.

Actually, Mr. Rectum, 1/3 is precisely equal to 0.3333...

With your obvious limitations, no one really expects you to understand, Mr. Rectum, but 0.3333... is an geometric series with an initial term of 0.3 and common ratio 0.1. As such we have:

0.333... = 0.3 / (1 - 0.1) = 1/3

See: https://en.wikipedia.org/wiki/Geometric_series

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Sunday, 8 August 2021 at 08:01:09 UTC-4, Eram semper recta wrote:
> Euler's vomit
>
> Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
>
> is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
>
> More here:
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

Euler is a grand embarrassment to Switzerland.

So many mistakes in his Elements Of Al-gibberish. Tsk, tsk.

söndag 8 augusti 2021 kl. 14:01:09 UTC+2 skrev Eram semper recta:
> Euler's vomit
>
> Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
>
> is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
>
> More here:
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
You are so jealous of him it is funny.

On Monday, 9 August 2021 at 01:21:35 UTC-4, zelos...@gmail.com wrote:
> söndag 8 augusti 2021 kl. 14:01:09 UTC+2 skrev Eram semper recta:
> > Euler's vomit
> >
> > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> >
> > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> >
> > More here:
> >
> > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> You are so jealous of him it is funny.

Jealous of his S = Lim S ? Ha, not a chance. Only an absolute birdbrain would make up such a definition, ill-formed in every respect.

måndag 9 augusti 2021 kl. 14:43:01 UTC+2 skrev Eram semper recta:
> On Monday, 9 August 2021 at 01:21:35 UTC-4, zelos...@gmail.com wrote:
> > söndag 8 augusti 2021 kl. 14:01:09 UTC+2 skrev Eram semper recta:
> > > Euler's vomit
> > >
> > > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> > >
> > > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> > >
> > > More here:
> > >
> > > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> > You are so jealous of him it is funny.
> Jealous of his S = Lim S ? Ha, not a chance. Only an absolute birdbrain would make up such a definition, ill-formed in every respect.
no one says S=lim S, as I have told you a thousand times, it is non-sense

On Tuesday, 10 August 2021 at 01:52:12 UTC-4, zelos...@gmail.com wrote:
> måndag 9 augusti 2021 kl. 14:43:01 UTC+2 skrev Eram semper recta:
> > On Monday, 9 August 2021 at 01:21:35 UTC-4, zelos...@gmail.com wrote:
> > > söndag 8 augusti 2021 kl. 14:01:09 UTC+2 skrev Eram semper recta:
> > > > Euler's vomit
> > > >
> > > > Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}
> > > >
> > > > is still taught in the shit lecture rooms of math worldwide. It's like an incurable virus that cannot be managed. Once infected, it becomes part of your brain DNA.
> > > >
> > > > More here:
> > > >
> > > > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> > > You are so jealous of him it is funny.
> > Jealous of his S = Lim S ? Ha, not a chance. Only an absolute birdbrain would make up such a definition, ill-formed in every respect.
> no one says S=lim S, as I have told you a thousand times, it is non-sense

Of course you do. 0.333... = 1/3 or 0.999... = 1 is classic S = Lim S. Just because you repeat your drivel a thousand times, do you think it will eventually become true? LMAO.

>Of course you do

Nope

>0.333... = 1/3 or 0.999... = 1 is classic S = Lim S

Nope, those are notations for the same elements

What you are trying to say is Lim {0.3,0.33,0.333,...} = 1/3 is your "S=Lim S" thing but it isn't

Lim {0.3,0.33,0.333,...}
this is your Lim S
so Lim S=S would mean you're saying

Lim {0.3,0.33,0.333,...}={0.3,0.33,0.333,...}

Which is incorrect, the limit of the sequence is not the sequence itself, but the rational number 1/3

On Wednesday, 11 August 2021 at 01:13:19 UTC-4, zelos...@gmail.com wrote:
> >Of course you do
>
> Nope
> >0.333... = 1/3 or 0.999... = 1 is classic S = Lim S
> Nope, those are notations for the same elements

They are not.

0.333... is a FAKE infinite sum.
1/3 is a well-formed number that is very well represented and meaningful.

0.333... is meaningless nonsense if interpreted as anything else besides a series.

>
> What you are trying to say is Lim {0.3,0.33,0.333,...} = 1/3 is your "S=Lim S" thing but it isn't

I am saying it and it is CORRECT. However, it was Euler who produced the blunder, not I!

https://www.academia.edu/45471184/Eulers_Blunder

>
> Lim {0.3,0.33,0.333,...}
> this is your Lim S
> so Lim S=S would mean you're saying
>
> Lim {0.3,0.33,0.333,...}={0.3,0.33,0.333,...}

No moron. Because I've never said anything like that.

Euler wrote:

Daher ist uns Bruch {Lim S} 1/(1+a) *****gleich***** dieser unendlichen Reihe 1 - a + aa - aaa + ... &c {S}.

===> S = Lim S

gleich in German means EQUAL.

>
> the limit of the sequence { Lim S } is not the sequence {S} itself, but the rational number 1/3

Of course! Classic S = Lim S. But only a crank like you refuses to learn!

>0.333... is a FAKE infinite sum.

It can be constructed with a series and it is a real one :) But that is only one of many ways.

>1/3 is a well-formed number that is very well represented and meaningful.

it is notation like all.

>No moron. Because I've never said anything like that.

Actually you did

Lim S = S

set S = {0.3,0.33,0.333,...}

Substitute
Lim {0.3,0.33,0.333,...} = {0.3,0.33,0.333,...}

That is exactly what you say.

On Thursday, 12 August 2021 at 01:17:21 UTC-4, zelos...@gmail.com wrote:
> >0.333... is a FAKE infinite sum.
> It can be constructed with a series and it is a real one :) But that is only one of many ways.

0.333... is not infinite in any sense of the word and is not a construction of an infinite series.

0.333... = \sum_{k=1}^{oo} 3/10^k

Your very own Rudin (who wrote the definitive mainstream book on real analysis) tells you that 0.333... is not at all obtained by an actual sum:

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

> >1/3 is a well-formed number that is very well represented and meaningful.
> it is notation like all.

It is meaningful notation, not your usual gibberish:

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

> Lim {0.3,0.33,0.333,...} = {0.3,0.33,0.333,...}

No moron. Once again, that is not what is being said at all by Euler.

Euler claims: 0.333... = \sum_{k=1}^{oo} 3/10^k = Lim_{n->oo} (1/3)x[1 - 10^(-n)] = 1/3

But any numbskull high school student can tell that \sum_{k=1}^{oo} 3/10^k and Lim_{n->oo} (1/3)x[1 - 10^(-n)] are two totally different things.

>0.333... is not infinite in any sense of the word and is not a construction of an infinite series.

It is notation and commonly viewed as such.

>Your very own Rudin (who wrote the definitive mainstream book on real analysis) tells you that 0.333... is not at all obtained by an actual sum:

I've read his book and knows what it says :) It is a series, aka a sequence of partial sums....just like the cauchy construction of real numbers. Coincidence?

>No moron. Once again, that is not what is being said at all by Euler.

That is what YOU are saying when you keep writin lim S=S

>Euler claims: 0.333... = \sum_{k=1}^{oo} 3/10^k = Lim_{n->oo} (1/3)x[1 - 10^(-n)] = 1/3

Which is not Lim S=S but Lim f(n)=r

Its a limit of a sum, so yes it is obtained from a sum:

0.333... = sum_{k=1}^{oo} 3/10^k

= lim_{n->oo} sum_{k=1}^{n} 3/10^k

= lim_{n->oo} 1/3 (1-10^(-n))

= 1/3

LMAO!

Eram semper recta schrieb am Donnerstag, 12. August 2021 um 13:32:42 UTC+2:
> On Thursday, 12 August 2021 at 01:17:21 UTC-4, zelos...@gmail.com wrote:
> > >0.333... is a FAKE infinite sum.
> > It can be constructed with a series and it is a real one :) But that is only one of many ways.
> 0.333... is not infinite in any sense of the word and is not a construction of an infinite series.
>
> 0.333... = \sum_{k=1}^{oo} 3/10^k
>
> Your very own Rudin (who wrote the definitive mainstream book on real analysis) tells you that 0.333... is not at all obtained by an actual sum:
>
> https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> > >1/3 is a well-formed number that is very well represented and meaningful.
> > it is notation like all.
> It is meaningful notation, not your usual gibberish:
>
> https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w
>
>
> > Lim {0.3,0.33,0.333,...} = {0.3,0.33,0.333,...}
>
> No moron. Once again, that is not what is being said at all by Euler.
>
> Euler claims: 0.333... = \sum_{k=1}^{oo} 3/10^k = Lim_{n->oo} (1/3)x[1 - 10^(-n)] = 1/3
>
> But any numbskull high school student can tell that \sum_{k=1}^{oo} 3/10^k and Lim_{n->oo} (1/3)x[1 - 10^(-n)] are two totally different things.

bird brain John Gabriel wrote:
> But any numbskull high school student can tell that sum_{k=1}^{oo} 3/10^k
and lim_{n->oo} (1/3)x[1 - 10^(-n)] are two totally different things.

What about the numbskull that doesn't know
sum_{k=1}^{oo} = lim_{n->oo} sum_{k=1}^{n}

Look into the mirror bird brain John Gabriel.
Grow up and get a life bird brain John Gabriel.

LoL

Mostowski Collapse schrieb am Freitag, 13. August 2021 um 12:49:20 UTC+2:
> Its a limit of a sum, so yes it is obtained from a sum:
> 0.333... = sum_{k=1}^{oo} 3/10^k
> = lim_{n->oo} sum_{k=1}^{n} 3/10^k
>
> = lim_{n->oo} 1/3 (1-10^(-n))
>
> = 1/3
>
> LMAO!
> Eram semper recta schrieb am Donnerstag, 12. August 2021 um 13:32:42 UTC+2:
> > On Thursday, 12 August 2021 at 01:17:21 UTC-4, zelos...@gmail.com wrote:
> > > >0.333... is a FAKE infinite sum.
> > > It can be constructed with a series and it is a real one :) But that is only one of many ways.
> > 0.333... is not infinite in any sense of the word and is not a construction of an infinite series.
> >
> > 0.333... = \sum_{k=1}^{oo} 3/10^k
> >
> > Your very own Rudin (who wrote the definitive mainstream book on real analysis) tells you that 0.333... is not at all obtained by an actual sum:
> >
> > https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
> > > >1/3 is a well-formed number that is very well represented and meaningful.
> > > it is notation like all.
> > It is meaningful notation, not your usual gibberish:
> >
> > https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w
> >
> >
> > > Lim {0.3,0.33,0.333,...} = {0.3,0.33,0.333,...}
> >
> > No moron. Once again, that is not what is being said at all by Euler.
> >
> > Euler claims: 0.333... = \sum_{k=1}^{oo} 3/10^k = Lim_{n->oo} (1/3)x[1 - 10^(-n)] = 1/3
> >
> > But any numbskull high school student can tell that \sum_{k=1}^{oo} 3/10^k and Lim_{n->oo} (1/3)x[1 - 10^(-n)] are two totally different things.