>The limit very much depends on n!

nope!

The limit is 1/3, I see no n there :)

>Look sonny: S(n)= (1/3) [1-10^(-n)]
>
>Lim_{n->3} S(n) = 0.333
>Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)

You really should try to learn these things properly.

>The thanks I get for educating you?

You have not educated me or anyone, only spread misfinformation.

>You just proved my point!

What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.

>I think you forget that I am not just "any person". Chuckle.

You are just like any narcissistic person, you are not special.

>That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!

You are so fucking juvenile, grow up.

To teach, you have to have knowledge to teach, you have none and I know way more than you :)

On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> >The limit very much depends on n!
> nope!
>
> The limit is 1/3, I see no n there :)

Look, stop being childish and if you carry on this way, I shall soon become bored with you.

You know full well how one arrives at 1/3.

GROW UP BOY!!!!!

<drivel follows>

> >Look sonny: S(n)= (1/3) [1-10^(-n)]
> >
> >Lim_{n->3} S(n) = 0.333
> >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
>
> You really should try to learn these things properly.
> >The thanks I get for educating you?
> You have not educated me or anyone, only spread misfinformation.
> >You just proved my point!
> What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> >I think you forget that I am not just "any person". Chuckle.
> You are just like any narcissistic person, you are not special.
> >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> You are so fucking juvenile, grow up.
>
> To teach, you have to have knowledge to teach, you have none and I know way more than you :)

onsdag 25 augusti 2021 kl. 17:10:03 UTC+2 skrev Eram semper recta:
> On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> > >The limit very much depends on n!
> > nope!
> >
> > The limit is 1/3, I see no n there :)
> Look, stop being childish and if you carry on this way, I shall soon become bored with you.
>
> You know full well how one arrives at 1/3.
>
> GROW UP BOY!!!!!
>
> <drivel follows>
> > >Look sonny: S(n)= (1/3) [1-10^(-n)]
> > >
> > >Lim_{n->3} S(n) = 0.333
> > >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
> >
> > You really should try to learn these things properly.
> > >The thanks I get for educating you?
> > You have not educated me or anyone, only spread misfinformation.
> > >You just proved my point!
> > What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> > >I think you forget that I am not just "any person". Chuckle.
> > You are just like any narcissistic person, you are not special.
> > >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> > You are so fucking juvenile, grow up.
> >
> > To teach, you have to have knowledge to teach, you have none and I know way more than you :)

I know how limits work, but the limit is independent of n, but the limit is taken over the variable n.

Learn the difference.

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.

On Thursday, 26 August 2021 at 01:31:44 UTC-4, zelos...@gmail.com wrote:
> onsdag 25 augusti 2021 kl. 17:10:03 UTC+2 skrev Eram semper recta:
> > On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> > > >The limit very much depends on n!
> > > nope!
> > >
> > > The limit is 1/3, I see no n there :)
> > Look, stop being childish and if you carry on this way, I shall soon become bored with you.
> >
> > You know full well how one arrives at 1/3.
> >
> > GROW UP BOY!!!!!
> >
> > <drivel follows>
> > > >Look sonny: S(n)= (1/3) [1-10^(-n)]
> > > >
> > > >Lim_{n->3} S(n) = 0.333
> > > >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
> > >
> > > You really should try to learn these things properly.
> > > >The thanks I get for educating you?
> > > You have not educated me or anyone, only spread misfinformation.
> > > >You just proved my point!
> > > What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> > > >I think you forget that I am not just "any person". Chuckle.
> > > You are just like any narcissistic person, you are not special.
> > > >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> > > You are so fucking juvenile, grow up.
> > >
> > > To teach, you have to have knowledge to teach, you have none and I know way more than you :)
> I know how limits work,

You know nothing about limit theory.

> but the limit is independent of n, but the limit is taken over the variable n.

Oh, you mean like THERE IS NOTHING CIRCULAR ABOUT c=f+g <=> g=c-f ?

LMAO.

<drivel>

On Thursday, 26 August 2021 at 01:31:44 UTC-4, zelos...@gmail.com wrote:
> onsdag 25 augusti 2021 kl. 17:10:03 UTC+2 skrev Eram semper recta:
> > On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> > > >The limit very much depends on n!
> > > nope!
> > >
> > > The limit is 1/3, I see no n there :)
> > Look, stop being childish and if you carry on this way, I shall soon become bored with you.
> >
> > You know full well how one arrives at 1/3.
> >
> > GROW UP BOY!!!!!
> >
> > <drivel follows>
> > > >Look sonny: S(n)= (1/3) [1-10^(-n)]
> > > >
> > > >Lim_{n->3} S(n) = 0.333
> > > >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
> > >
> > > You really should try to learn these things properly.
> > > >The thanks I get for educating you?
> > > You have not educated me or anyone, only spread misfinformation.
> > > >You just proved my point!
> > > What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> > > >I think you forget that I am not just "any person". Chuckle.
> > > You are just like any narcissistic person, you are not special.
> > > >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> > > You are so fucking juvenile, grow up.
> > >
> > > To teach, you have to have knowledge to teach, you have none and I know way more than you :)
> I know how limits work, but the limit is independent of n, but the limit is taken over the variable n.
>
> Learn the difference.

Oh, you mean like "c=f+g <=> g=c-f is CIRCULAR" ?

LMAO.

<drivel>

torsdag 26 augusti 2021 kl. 12:44:12 UTC+2 skrev New Age Prophet:
> On Thursday, 26 August 2021 at 01:31:44 UTC-4, zelos...@gmail.com wrote:
> > onsdag 25 augusti 2021 kl. 17:10:03 UTC+2 skrev Eram semper recta:
> > > On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> > > > >The limit very much depends on n!
> > > > nope!
> > > >
> > > > The limit is 1/3, I see no n there :)
> > > Look, stop being childish and if you carry on this way, I shall soon become bored with you.
> > >
> > > You know full well how one arrives at 1/3.
> > >
> > > GROW UP BOY!!!!!
> > >
> > > <drivel follows>
> > > > >Look sonny: S(n)= (1/3) [1-10^(-n)]
> > > > >
> > > > >Lim_{n->3} S(n) = 0.333
> > > > >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
> > > >
> > > > You really should try to learn these things properly.
> > > > >The thanks I get for educating you?
> > > > You have not educated me or anyone, only spread misfinformation.
> > > > >You just proved my point!
> > > > What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> > > > >I think you forget that I am not just "any person". Chuckle.
> > > > You are just like any narcissistic person, you are not special.
> > > > >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> > > > You are so fucking juvenile, grow up.
> > > >
> > > > To teach, you have to have knowledge to teach, you have none and I know way more than you :)
> > I know how limits work, but the limit is independent of n, but the limit is taken over the variable n.
> >
> > Learn the difference.
> Oh, you mean like "c=f+g <=> g=c-f is CIRCULAR" ?
>
> LMAO.
>
> <drivel>

That is what you say :)

On Friday, 27 August 2021 at 01:02:40 UTC-4, zelos...@gmail.com wrote:
> torsdag 26 augusti 2021 kl. 12:44:12 UTC+2 skrev New Age Prophet:
> > On Thursday, 26 August 2021 at 01:31:44 UTC-4, zelos...@gmail.com wrote:
> > > onsdag 25 augusti 2021 kl. 17:10:03 UTC+2 skrev Eram semper recta:
> > > > On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> > > > > >The limit very much depends on n!
> > > > > nope!
> > > > >
> > > > > The limit is 1/3, I see no n there :)
> > > > Look, stop being childish and if you carry on this way, I shall soon become bored with you.
> > > >
> > > > You know full well how one arrives at 1/3.
> > > >
> > > > GROW UP BOY!!!!!
> > > >
> > > > <drivel follows>
> > > > > >Look sonny: S(n)= (1/3) [1-10^(-n)]
> > > > > >
> > > > > >Lim_{n->3} S(n) = 0.333
> > > > > >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
> > > > >
> > > > > You really should try to learn these things properly.
> > > > > >The thanks I get for educating you?
> > > > > You have not educated me or anyone, only spread misfinformation.
> > > > > >You just proved my point!
> > > > > What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> > > > > >I think you forget that I am not just "any person". Chuckle.
> > > > > You are just like any narcissistic person, you are not special.
> > > > > >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> > > > > You are so fucking juvenile, grow up.
> > > > >
> > > > > To teach, you have to have knowledge to teach, you have none and I know way more than you :)
> > > I know how limits work, but the limit is independent of n, but the limit is taken over the variable n.
> > >
> > > Learn the difference.
> > Oh, you mean like "c=f+g <=> g=c-f is CIRCULAR" ?
> >
> > LMAO.
> >
> > <drivel>
> That is what you say :)

Au contraire! That is what Jean Pierre Messager (aka Python) said and you stepped right into the SHIT!! LMAO.

Can anything get more cranky than claiming that "if c=f+g then g=c-f is circular" ? LMAO

You went along with that delusional psychopath Jean Pierre Messager (aka Python).

That is what YOU said! You are a crank! Here it is again with link following:

***************************************************************
> > He think that stuff you point out is circular
> >
> > if c=f+g
> > then g=c-f
> > so circular!
***************************************************************

https://groups.google.com/g/sci.math/c/QMhqLZH1434/m/vAEmniRtBwAJ

torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > >
> > > > > > > > >You DO CARE!
> > > > > > > >
> > > > > > > > I do not
> > > > > > > > >You still obey S = Lim S.
> > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > S=Lim S
> > > > > > > > Substitute
> > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > >
> > > > > > > > Is pure nonsense.
> > > > > > > >
> > > > > > > > What we have is S=lim S_n
> > > > > > > >
> > > > > > > > HUGE difference.
> > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > >
> > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > >
> > > > > > > Fits you and Klyver perfectly!
> > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > >
> > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > Why do you like to omit the subscript?
> > > > >
> > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > >
> > > > > The series IS its nth partial sum. Nothing else.
> > > > >
> > > > > >
> > > > > > It's S=lim S_n.
> > > > >
> > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > Not at all. That is how you would like it to be, but the reality is very different.
> > >
> > > A series is NOT an infinite sum.
> > > >
> > > > The series is defined as the limit of the partial sums S_n.
> > > >
> > > > Hence S = lim_n S_n.
> > > Right. S = Lim S. No difference.
> > > >
> > > > S = lim_n S is trivially the since S does not depend on n.
> > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > >
> > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
>
> > S depends on its partial sums, but not on n.
> Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
>
> The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
>
> There is no S = S_inf. That's just nonsense.
> >
> > It is lim_n S_n = S.
> NO. Lim S is very well defined to be 1/3 in the case of 0.333...
>
> All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
S=lim_n S_n=1/3=0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...

No contradictions here.

On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > >
> > > > > > > > > >You DO CARE!
> > > > > > > > >
> > > > > > > > > I do not
> > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > S=Lim S
> > > > > > > > > Substitute
> > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > >
> > > > > > > > > Is pure nonsense.
> > > > > > > > >
> > > > > > > > > What we have is S=lim S_n
> > > > > > > > >
> > > > > > > > > HUGE difference.
> > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > >
> > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > >
> > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > >
> > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > Why do you like to omit the subscript?
> > > > > >
> > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > >
> > > > > > The series IS its nth partial sum. Nothing else.
> > > > > >
> > > > > > >
> > > > > > > It's S=lim S_n.
> > > > > >
> > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > >
> > > > A series is NOT an infinite sum.
> > > > >
> > > > > The series is defined as the limit of the partial sums S_n.
> > > > >
> > > > > Hence S = lim_n S_n.
> > > > Right. S = Lim S. No difference.
> > > > >
> > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > >
> > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> >
> > > S depends on its partial sums, but not on n.
> > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> >
> > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> >
> > There is no S = S_inf. That's just nonsense.
> > >
> > > It is lim_n S_n = S.
> > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> >
> > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> S=lim_n S_n =1/3

Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.

> =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...

Bullshit. S = 0.333.... Lim S = 1/3

>
> No contradictions here.

Right, only your garbage.

fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail..com wrote:
> > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > >
> > > > > > > > > > >You DO CARE!
> > > > > > > > > >
> > > > > > > > > > I do not
> > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > S=Lim S
> > > > > > > > > > Substitute
> > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0..1111,...)
> > > > > > > > > >
> > > > > > > > > > Is pure nonsense.
> > > > > > > > > >
> > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > >
> > > > > > > > > > HUGE difference.
> > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > >
> > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > >
> > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > >
> > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > Why do you like to omit the subscript?
> > > > > > >
> > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > >
> > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > >
> > > > > > > >
> > > > > > > > It's S=lim S_n.
> > > > > > >
> > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > >
> > > > > A series is NOT an infinite sum.
> > > > > >
> > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > >
> > > > > > Hence S = lim_n S_n.
> > > > > Right. S = Lim S. No difference.
> > > > > >
> > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > >
> > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > >
> > > > S depends on its partial sums, but not on n.
> > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > >
> > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > >
> > > There is no S = S_inf. That's just nonsense.
> > > >
> > > > It is lim_n S_n = S.
> > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > >
> > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > S=lim_n S_n =1/3
> Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> Bullshit. S = 0.333.... Lim S = 1/3
>
> >
> > No contradictions here.
>
> Right, only your garbage.
S and lim_n S_n are the same object by definition.

On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail..com wrote:
> > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333....
> > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > >
> > > > > > > > > > > >You DO CARE!
> > > > > > > > > > >
> > > > > > > > > > > I do not
> > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > S=Lim S
> > > > > > > > > > > Substitute
> > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > >
> > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > >
> > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > >
> > > > > > > > > > > HUGE difference.
> > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > >
> > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > >
> > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > >
> > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > Why do you like to omit the subscript?
> > > > > > > >
> > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > >
> > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > >
> > > > > > > > >
> > > > > > > > > It's S=lim S_n.
> > > > > > > >
> > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > >
> > > > > > A series is NOT an infinite sum.
> > > > > > >
> > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > >
> > > > > > > Hence S = lim_n S_n.
> > > > > > Right. S = Lim S. No difference.
> > > > > > >
> > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > >
> > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > >
> > > > > S depends on its partial sums, but not on n.
> > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > >
> > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > >
> > > > There is no S = S_inf. That's just nonsense.
> > > > >
> > > > > It is lim_n S_n = S.
> > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > > >
> > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > S=lim_n S_n =1/3
> > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> > Bullshit. S = 0.333.... Lim S = 1/3
> >
> > >
> > > No contradictions here.
> >
> > Right, only your garbage.
> S and lim_n S_n are the same object by definition.

Changing your tune again?

No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.

lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos....@gmail.com wrote:
> > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > >
> > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > >
> > > > > > > > > > > > I do not
> > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > Substitute
> > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > >
> > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > >
> > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > >
> > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S..
> > > > > > > > > > >
> > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > >
> > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > >
> > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > >
> > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > >
> > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > It's S=lim S_n.
> > > > > > > > >
> > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > >
> > > > > > > A series is NOT an infinite sum.
> > > > > > > >
> > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > >
> > > > > > > > Hence S = lim_n S_n.
> > > > > > > Right. S = Lim S. No difference.
> > > > > > > >
> > > > > > > > S = lim_n S is trivially the since S does not depend on n..
> > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > >
> > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > >
> > > > > > S depends on its partial sums, but not on n.
> > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > >
> > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > >
> > > > > There is no S = S_inf. That's just nonsense.
> > > > > >
> > > > > > It is lim_n S_n = S.
> > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > > > >
> > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > S=lim_n S_n =1/3
> > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> > > Bullshit. S = 0.333.... Lim S = 1/3
> > >
> > > >
> > > > No contradictions here.
> > >
> > > Right, only your garbage.
> > S and lim_n S_n are the same object by definition.
> Changing your tune again?
>
> No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
They are exactly the same thing by definition.

S := lim_n S_n.

On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail..com wrote:
> > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos....@gmail.com wrote:
> > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > >
> > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > >
> > > > > > > > > > > > > I do not
> > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0..111,0.1111,...)
> > > > > > > > > > > > >
> > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > >
> > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > >
> > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > >
> > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > >
> > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > >
> > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > >
> > > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > >
> > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > >
> > > > > > > > A series is NOT an infinite sum.
> > > > > > > > >
> > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > >
> > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > >
> > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > >
> > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > >
> > > > > > > S depends on its partial sums, but not on n.
> > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > >
> > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > >
> > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > >
> > > > > > > It is lim_n S_n = S.
> > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333....
> > > > > >
> > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > S=lim_n S_n =1/3
> > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > >
> > > > >
> > > > > No contradictions here.
> > > >
> > > > Right, only your garbage.
> > > S and lim_n S_n are the same object by definition.
> > Changing your tune again?
> >
> > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> They are exactly the same thing by definition.
>
> S := lim_n S_n.

You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.

lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> > lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus....@gmail.com wrote:
> > > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I do not
> > > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit..
> > > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > > >
> > > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > > >
> > > > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > > > >
> > > > > > > > > > > >
> > > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > > >
> > > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > > >
> > > > > > > > > A series is NOT an infinite sum.
> > > > > > > > > >
> > > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > > >
> > > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > > >
> > > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > > >
> > > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > > >
> > > > > > > > S depends on its partial sums, but not on n.
> > > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > > >
> > > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > > >
> > > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > > >
> > > > > > > > It is lim_n S_n = S.
> > > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333....
> > > > > > >
> > > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > > S=lim_n S_n =1/3
> > > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> > > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > > >
> > > > > >
> > > > > > No contradictions here.
> > > > >
> > > > > Right, only your garbage.
> > > > S and lim_n S_n are the same object by definition.
> > > Changing your tune again?
> > >
> > > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> > They are exactly the same thing by definition.
> >
> > S := lim_n S_n.
> You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.
A series *is* a number, or a function that gives numbers for every x.

On Saturday, August 28, 2021 at 9:03:31 AM UTC-7, Eram semper recta wrote:
> > They are exactly the same thing by definition.
> >
> > S := lim_n S_n.
> You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.

That's what model theory is for number theory.

Perhaps if the trolllll always had angle brackets about its' semi-defined terms,
what where they're usually some "fright quotes" of a sort: that's what a usual
conscientious mimicry would be for, here is for understanding that it's a poor
deluded thing, or perhaps with a terrible communication pathology, ....

Ah, I see it's started adding them....

(That model theory makes for models of numbers by value in real numbers mostly,
and that descriptive set theory and topology result simple clear, closed models
mostly, here for real-valued variables.)

On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
> lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> > On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> > > lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > > > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus....@gmail.com wrote:
> > > > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > I do not
> > > > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > > > >
> > > > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > > > >
> > > > > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > > > > >
> > > > > > > > > > > > >
> > > > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > > > >
> > > > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > > > >
> > > > > > > > > > A series is NOT an infinite sum.
> > > > > > > > > > >
> > > > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > > > >
> > > > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > > > >
> > > > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > > > >
> > > > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > > > >
> > > > > > > > > S depends on its partial sums, but not on n.
> > > > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > > > >
> > > > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > > > >
> > > > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > > > >
> > > > > > > > > It is lim_n S_n = S.
> > > > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > > > > > > >
> > > > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > > > S=lim_n S_n =1/3
> > > > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> > > > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > > > >
> > > > > > >
> > > > > > > No contradictions here.
> > > > > >
> > > > > > Right, only your garbage.
> > > > > S and lim_n S_n are the same object by definition.
> > > > Changing your tune again?
> > > >
> > > > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> > > They are exactly the same thing by definition.
> > >
> > > S := lim_n S_n.
> > You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.
> A series *is* a number,

söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
> On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
> > lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> > > On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> > > > lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > > > > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > > > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > I do not
> > > > > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,....)
> > > > > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > > > > >
> > > > > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > > > > >
> > > > > > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > > > > >
> > > > > > > > > > > A series is NOT an infinite sum.
> > > > > > > > > > > >
> > > > > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > > > > >
> > > > > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > > > > >
> > > > > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > > > > >
> > > > > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > > > > >
> > > > > > > > > > S depends on its partial sums, but not on n.
> > > > > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > > > > >
> > > > > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > > > > >
> > > > > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > > > > >
> > > > > > > > > > It is lim_n S_n = S.
> > > > > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0..333...
> > > > > > > > >
> > > > > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > > > > S=lim_n S_n =1/3
> > > > > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> > > > > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > > > > >
> > > > > > > >
> > > > > > > > No contradictions here.
> > > > > > >
> > > > > > > Right, only your garbage.
> > > > > > S and lim_n S_n are the same object by definition.
> > > > > Changing your tune again?
> > > > >
> > > > > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> > > > They are exactly the same thing by definition.
> > > >
> > > > S := lim_n S_n.
> > > You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.
> > A series *is* a number,
> Nope. A series is not a number.
>
> "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity." - The wikipedia moronica
>
> In other words, it cannot ever be a number because "adding infinitely many quantities" is a dream, in other words a super task which is impossible. LMAO.
>
> Look idiot, Euler defined it this way S = Lim S:
>
> Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+.... &c.
>
> Only the dumbest mainstream academics are still arguing.
> > or a function that gives numbers for every x.
> What?! LMAO.
A series is a number (or a function that gives numbers). For example, Taylor series takes real numbers x and gives out a real number.

On Sunday, 29 August 2021 at 10:12:02 UTC-4, markus...@gmail.com wrote:
> söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
> > On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
> > > lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> > > > On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> > > > > lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > > > > > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > > > > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > > > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus....@gmail.com wrote:
> > > > > > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > > > > > That is why everything you have is shit. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > I do not
> > > > > > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,....)
> > > > > > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > > > > > >You mean what YOU think matters. Chuckle..
> > > > > > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > The series IS its nth partial sum. Nothing else..
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > > > > > >
> > > > > > > > > > > > A series is NOT an infinite sum.
> > > > > > > > > > > > >
> > > > > > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > > > > > >
> > > > > > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > > > > > >
> > > > > > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > > > > > >
> > > > > > > > > > > S depends on its partial sums, but not on n.
> > > > > > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > > > > > >
> > > > > > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > > > > > >
> > > > > > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > > > > > >
> > > > > > > > > > > It is lim_n S_n = S.
> > > > > > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > > > > > > > > >
> > > > > > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > > > > > S=lim_n S_n =1/3
> > > > > > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ....
> > > > > > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > > > > > >
> > > > > > > > >
> > > > > > > > > No contradictions here.
> > > > > > > >
> > > > > > > > Right, only your garbage.
> > > > > > > S and lim_n S_n are the same object by definition.
> > > > > > Changing your tune again?
> > > > > >
> > > > > > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> > > > > They are exactly the same thing by definition.
> > > > >
> > > > > S := lim_n S_n.
> > > > You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.
> > > A series *is* a number,
> > Nope. A series is not a number.
> >
> > "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity." - The wikipedia moronica
> >
> > In other words, it cannot ever be a number because "adding infinitely many quantities" is a dream, in other words a super task which is impossible.. LMAO.
> >
> > Look idiot, Euler defined it this way S = Lim S:
> >
> > Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+.... &c.
> >
> > Only the dumbest mainstream academics are still arguing.
> > > or a function that gives numbers for every x.
> > What?! LMAO.
> A series is a number (or a function that gives numbers).

söndag 29 augusti 2021 kl. 20:08:19 UTC+2 skrev Eram semper recta:
> On Sunday, 29 August 2021 at 10:12:02 UTC-4, markus...@gmail.com wrote:
> > söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
> > > On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
> > > > lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> > > > > On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> > > > > > lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > > > > > > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > > > > > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > > > > > > That is why everything you have is shit.. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > I do not
> > > > > > > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > > > > > > >
> > > > > > > > > > > > > A series is NOT an infinite sum.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > > > > > > >
> > > > > > > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > > > > > > >
> > > > > > > > > > > > S depends on its partial sums, but not on n.
> > > > > > > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > > > > > > >
> > > > > > > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > > > > > > >
> > > > > > > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > > > > > > >
> > > > > > > > > > > > It is lim_n S_n = S.
> > > > > > > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > > > > > > > > > >
> > > > > > > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > > > > > > S=lim_n S_n =1/3
> > > > > > > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > > > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ....
> > > > > > > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > No contradictions here.
> > > > > > > > >
> > > > > > > > > Right, only your garbage.
> > > > > > > > S and lim_n S_n are the same object by definition.
> > > > > > > Changing your tune again?
> > > > > > >
> > > > > > > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> > > > > > They are exactly the same thing by definition.
> > > > > >
> > > > > > S := lim_n S_n.
> > > > > You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.
> > > > A series *is* a number,
> > > Nope. A series is not a number.
> > >
> > > "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity." - The wikipedia moronica
> > >
> > > In other words, it cannot ever be a number because "adding infinitely many quantities" is a dream, in other words a super task which is impossible. LMAO.
> > >
> > > Look idiot, Euler defined it this way S = Lim S:
> > >
> > > Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+... &c.
> > >
> > > Only the dumbest mainstream academics are still arguing.
> > > > or a function that gives numbers for every x.
> > > What?! LMAO.
> > A series is a number (or a function that gives numbers).
> No, idiot. NO.
> > For example, Taylor series takes real numbers x and gives out a real number.
> A Taylor series (which is hopelessly inferior to the Gabriel Polynomial) never produces anything but a rational number approximation.

fredag 27 augusti 2021 kl. 12:40:52 UTC+2 skrev Eram semper recta:
> On Friday, 27 August 2021 at 01:02:40 UTC-4, zelos...@gmail.com wrote:
> > torsdag 26 augusti 2021 kl. 12:44:12 UTC+2 skrev New Age Prophet:
> > > On Thursday, 26 August 2021 at 01:31:44 UTC-4, zelos...@gmail.com wrote:
> > > > onsdag 25 augusti 2021 kl. 17:10:03 UTC+2 skrev Eram semper recta:
> > > > > On Wednesday, 25 August 2021 at 01:20:41 UTC-4, zelos...@gmail.com wrote:
> > > > > > >The limit very much depends on n!
> > > > > > nope!
> > > > > >
> > > > > > The limit is 1/3, I see no n there :)
> > > > > Look, stop being childish and if you carry on this way, I shall soon become bored with you.
> > > > >
> > > > > You know full well how one arrives at 1/3.
> > > > >
> > > > > GROW UP BOY!!!!!
> > > > >
> > > > > <drivel follows>
> > > > > > >Look sonny: S(n)= (1/3) [1-10^(-n)]
> > > > > > >
> > > > > > >Lim_{n->3} S(n) = 0.333
> > > > > > >Lim_{n->oo} S(n) = 0.333... (at least according to your bogus mathematics!)
> > > > > >
> > > > > > You really should try to learn these things properly.
> > > > > > >The thanks I get for educating you?
> > > > > > You have not educated me or anyone, only spread misfinformation.
> > > > > > >You just proved my point!
> > > > > > What point? That I despise you for being such a fucking narcissist? I cannot stand narcissists like you.
> > > > > > >I think you forget that I am not just "any person". Chuckle.
> > > > > > You are just like any narcissistic person, you are not special.
> > > > > > >That can't be true because someone I know from Oops-Allah (Uppsala university) can't be taught at all!
> > > > > > You are so fucking juvenile, grow up.
> > > > > >
> > > > > > To teach, you have to have knowledge to teach, you have none and I know way more than you :)
> > > > I know how limits work, but the limit is independent of n, but the limit is taken over the variable n.
> > > >
> > > > Learn the difference.
> > > Oh, you mean like "c=f+g <=> g=c-f is CIRCULAR" ?
> > >
> > > LMAO.
> > >
> > > <drivel>
> > That is what you say :)
> Au contraire! That is what Jean Pierre Messager (aka Python) said and you stepped right into the SHIT!! LMAO.
>
> Can anything get more cranky than claiming that "if c=f+g then g=c-f is circular" ? LMAO
>
> You went along with that delusional psychopath Jean Pierre Messager (aka Python).
>
> That is what YOU said! You are a crank! Here it is again with link following:
>
> ***************************************************************
> > > He think that stuff you point out is circular
> > >
> > > if c=f+g
> > > then g=c-f
> > > so circular!
> ***************************************************************
>
> https://groups.google.com/g/sci.math/c/QMhqLZH1434/m/vAEmniRtBwAJ
I pointed out that is how YOU think. Not that I think it you dishonest lying sack of shit :)

söndag 29 augusti 2021 kl. 20:08:19 UTC+2 skrev Eram semper recta:
> On Sunday, 29 August 2021 at 10:12:02 UTC-4, markus...@gmail.com wrote:
> > söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
> > > On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
> > > > lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> > > > > On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> > > > > > lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> > > > > > > On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> > > > > > > > fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > On Wednesday, 18 August 2021 at 10:53:34 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > > onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 19:28:57 UTC-4, markus...@gmail.com wrote:
> > > > > > > > > > > > > > > > tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper recta:
> > > > > > > > > > > > > > > > > On Tuesday, 17 August 2021 at 03:35:11 UTC-4, zelos...@gmail.com wrote:
> > > > > > > > > > > > > > > > > > >It is a WELL-FORMED NAME, unlike the bullshit 0.333...
> > > > > > > > > > > > > > > > > > no, it's name is Bob, we write it as 1/3
> > > > > > > > > > > > > > > > > > >Well, if one builds on shit, the end result is always shit.
> > > > > > > > > > > > > > > > > > That is why everything you have is shit.. But the cauchy constructions are valid and works fine.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > >You DO CARE!
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > I do not
> > > > > > > > > > > > > > > > > > >You still obey S = Lim S.
> > > > > > > > > > > > > > > > > > nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > > > > S=Lim S
> > > > > > > > > > > > > > > > > > Substitute
> > > > > > > > > > > > > > > > > > (0,0.1,0.11,0.111,0.1111,...)=Lim (0,0.1,0.11,0.111,0.1111,...)
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Is pure nonsense.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > What we have is S=lim S_n
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > HUGE difference.
> > > > > > > > > > > > > > > > > > >Your student Markus Klyver recently admitted it - not that it matters much because he is a moron just like you.
> > > > > > > > > > > > > > > > > > He has admitted that S=lim S_n, not your shit.
> > > > > > > > > > > > > > > > > S = Lim S_n is EXACTLY what is meant by S = Lim S.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Crank: One who cannot be convinced in the face of overwhelming evidence.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Fits you and Klyver perfectly!
> > > > > > > > > > > > > > > > > > >Of course what Euler wrote is of importance. Didn't you just say "build on the same foundational ideas"? You pathetic, stupid crank!
> > > > > > > > > > > > > > > > > > The ideas he wrote is what matters, if he miswrote somewhere is much less important.
> > > > > > > > > > > > > > > > > > >You mean what YOU think matters. Chuckle.
> > > > > > > > > > > > > > > > > > That is what matters to the mathematical community, of which you are not part.
> > > > > > > > > > > > > > > > > > >See, no answer because you know I am right!!!
> > > > > > > > > > > > > > > > > > Ah so by not addressing most of the things I post to you, you admit here that I am right then.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Or are you gonna do cherry picking/be a hypocrite and say it is suddenly different for you?
> > > > > > > > > > > > > > > > Why do you like to omit the subscript?
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > S=lim S is bad notation since the right hand side depends on n, whereas the left hand side has no dependence on n.
> > > > > > > > > > > > > > > The left hand side IS dependent on the right hand side. It is the LIMIT of the series S. The limit is very much dependent on n and also how it is realised in analysis.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > The series IS its nth partial sum. Nothing else.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > It's S=lim S_n.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Grow a brain, you idiot! Suddenly you're worried about notation? LMAO.
> > > > > > > > > > > > > > The limit of the series (which is a constant) is the series itself, but that not how the series is defined.
> > > > > > > > > > > > > Not at all. That is how you would like it to be, but the reality is very different.
> > > > > > > > > > > > >
> > > > > > > > > > > > > A series is NOT an infinite sum.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > The series is defined as the limit of the partial sums S_n.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Hence S = lim_n S_n.
> > > > > > > > > > > > > Right. S = Lim S. No difference.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > S = lim_n S is trivially the since S does not depend on n.
> > > > > > > > > > > > > S very much depends on its partial sums defined by S(n)=(1/3)[1-10^(-n)].
> > > > > > > > > > > > >
> > > > > > > > > > > > > S is defined by its partial sums. There is no such thing as an infinite S or even a unique S.
> > > > > > > > > > >
> > > > > > > > > > > > S depends on its partial sums, but not on n.
> > > > > > > > > > > Not quite correct. S depends on its nth partial sum as defined by S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n too, because the limit is realised by considering what happens as n becomes very large.
> > > > > > > > > > >
> > > > > > > > > > > The limit is a very clear concept. S is not infinite and CANNOT be defined in ANY other way, except by its partial sums. If you think otherwise, then you would have to show me ALL of S. You can't.
> > > > > > > > > > >
> > > > > > > > > > > There is no S = S_inf. That's just nonsense.
> > > > > > > > > > > >
> > > > > > > > > > > > It is lim_n S_n = S.
> > > > > > > > > > > NO. Lim S is very well defined to be 1/3 in the case of 0.333...
> > > > > > > > > > >
> > > > > > > > > > > All you've had so far is hand waving and excuses which for the most part are not even relevant to the discussion. You are trying to distract from the main topic which is the FACT that Euler defined S = Lim S and moreover that it was a very big blunder!
> > > > > > > > > > S=lim_n S_n =1/3
> > > > > > > > > Nope. S is a series. Lim_n S_n is the number 1/3. Two totally different objects, therefore cannot be equal.
> > > > > > > > > > =0.333... if (S_n) is the sequence 0.3, 0.33, 0.333, ....
> > > > > > > > > Bullshit. S = 0.333.... Lim S = 1/3
> > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > No contradictions here.
> > > > > > > > >
> > > > > > > > > Right, only your garbage.
> > > > > > > > S and lim_n S_n are the same object by definition.
> > > > > > > Changing your tune again?
> > > > > > >
> > > > > > > No. S and Lim_n S_n are two different things. Your ill-formed definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> > > > > > They are exactly the same thing by definition.
> > > > > >
> > > > > > S := lim_n S_n.
> > > > > You just don' get it, do you? You cannot say that a <series> is equal to a <number> because they are two different objects. You're such a moron.
> > > > A series *is* a number,
> > > Nope. A series is not a number.
> > >
> > > "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity." - The wikipedia moronica
> > >
> > > In other words, it cannot ever be a number because "adding infinitely many quantities" is a dream, in other words a super task which is impossible. LMAO.
> > >
> > > Look idiot, Euler defined it this way S = Lim S:
> > >
> > > Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+... &c.
> > >
> > > Only the dumbest mainstream academics are still arguing.
> > > > or a function that gives numbers for every x.
> > > What?! LMAO.
> > A series is a number (or a function that gives numbers).
> No, idiot. NO.
> > For example, Taylor series takes real numbers x and gives out a real number.
> A Taylor series (which is hopelessly inferior to the Gabriel Polynomial) never produces anything but a rational number approximation.

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 was a preeminent mainstream crank like most on this newsgroup.

Eram semper recta explained on 8/29/2021 :
> On Sunday, 29 August 2021 at 10:12:02 UTC-4, markus...@gmail.com wrote:
>> söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
>>> On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
>>>> lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
>>>>> On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
>>>>>> lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
>>>>>>> On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
>>>>>>>> fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
>>>>>>>>> On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com
>>>>>>>>> wrote:
>>>>>>>>>> torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
>>>>>>>>>>> On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com
>>>>>>>>>>> wrote:
>>>>>>>>>>>> onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
>>>>>>>>>>>>> On Wednesday, 18 August 2021 at 10:53:34 UTC-4,
>>>>>>>>>>>>> markus...@gmail.com wrote:
>>>>>>>>>>>>>> onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper
>>>>>>>>>>>>>> recta:
>>>>>>>>>>>>>>> On Tuesday, 17 August 2021 at 19:28:57 UTC-4,
>>>>>>>>>>>>>>> markus...@gmail.com wrote:
>>>>>>>>>>>>>>>> tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper
>>>>>>>>>>>>>>>> recta:
>>>>>>>>>>>>>>>>> On Tuesday, 17 August 2021 at 03:35:11 UTC-4,
>>>>>>>>>>>>>>>>> zelos...@gmail.com wrote:
>>>>>>>>>>>>>>>>>>> It is a WELL-FORMED NAME, unlike the bullshit 0.333... no,
>>>>>>>>>>>>>>>>>>> it's name is Bob, we write it as 1/3 Well, if one builds
>>>>>>>>>>>>>>>>>>> on shit, the end result is always shit.
>>>>>>>>>>>>>>>>>> That is why everything you have is shit. But the cauchy
>>>>>>>>>>>>>>>>>> constructions are valid and works fine.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> You DO CARE!
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I do not
>>>>>>>>>>>>>>>>>>> You still obey S = Lim S.
>>>>>>>>>>>>>>>>>> nope, again S=(0,0.1,0.11,0.111,0.1111,...)
>>>>>>>>>>>>>>>>>> S=Lim S
>>>>>>>>>>>>>>>>>> Substitute
>>>>>>>>>>>>>>>>>> (0,0.1,0.11,0.111,0.1111,...)=Lim
>>>>>>>>>>>>>>>>>> (0,0.1,0.11,0.111,0.1111,...)
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Is pure nonsense.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> What we have is S=lim S_n
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> HUGE difference.
>>>>>>>>>>>>>>>>>>> Your student Markus Klyver recently admitted it - not that
>>>>>>>>>>>>>>>>>>> it matters much because he is a moron just like you.
>>>>>>>>>>>>>>>>>> He has admitted that S=lim S_n, not your shit.
>>>>>>>>>>>>>>>>> S = Lim S_n is EXACTLY what is meant by S = Lim S.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Crank: One who cannot be convinced in the face of
>>>>>>>>>>>>>>>>> overwhelming evidence.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Fits you and Klyver perfectly!
>>>>>>>>>>>>>>>>>>> Of course what Euler wrote is of importance. Didn't you
>>>>>>>>>>>>>>>>>>> just say "build on the same foundational ideas"? You
>>>>>>>>>>>>>>>>>>> pathetic, stupid crank! The ideas he wrote is what
>>>>>>>>>>>>>>>>>>> matters, if he miswrote somewhere is much less important.
>>>>>>>>>>>>>>>>>>> You mean what YOU think matters. Chuckle. That is what
>>>>>>>>>>>>>>>>>>> matters to the mathematical community, of which you are not
>>>>>>>>>>>>>>>>>>> part. See, no answer because you know I am right!!!
>>>>>>>>>>>>>>>>>> Ah so by not addressing most of the things I post to you,
>>>>>>>>>>>>>>>>>> you admit here that I am right then.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Or are you gonna do cherry picking/be a hypocrite and say it
>>>>>>>>>>>>>>>>>> is suddenly different for you?
>>>>>>>>>>>>>>>> Why do you like to omit the subscript?
>>>>>>>>>>>>>>>> S=lim S is bad notation since the right hand side depends on
>>>>>>>>>>>>>>>> n, whereas the left hand side has no dependence on n.
>>>>>>>>>>>>>>> The left hand side IS dependent on the right hand side. It is
>>>>>>>>>>>>>>> the LIMIT of the series S. The limit is very much dependent on
>>>>>>>>>>>>>>> n and also how it is realised in analysis.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The series IS its nth partial sum. Nothing else.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It's S=lim S_n.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Grow a brain, you idiot! Suddenly you're worried about
>>>>>>>>>>>>>>> notation? LMAO.
>>>>>>>>>>>>>> The limit of the series (which is a constant) is the series
>>>>>>>>>>>>>> itself, but that not how the series is defined.
>>>>>>>>>>>>> Not at all. That is how you would like it to be, but the reality
>>>>>>>>>>>>> is very different.
>>>>>>>>>>>>>
>>>>>>>>>>>>> A series is NOT an infinite sum.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The series is defined as the limit of the partial sums S_n.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hence S = lim_n S_n. Right. S = Lim S. No difference.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> S = lim_n S is trivially the since S does not depend on n.
>>>>>>>>>>>>> S very much depends on its partial sums defined by
>>>>>>>>>>>>> S(n)=(1/3)[1-10^(-n)].
>>>>>>>>>>>>>
>>>>>>>>>>>>> S is defined by its partial sums. There is no such thing as an
>>>>>>>>>>>>> infinite S or even a unique S.
>>>>>>>>>>>> S depends on its partial sums, but not on n.
>>>>>>>>>>> Not quite correct. S depends on its nth partial sum as defined by
>>>>>>>>>>> S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n
>>>>>>>>>>> too, because the limit is realised by considering what happens as n
>>>>>>>>>>> becomes very large.
>>>>>>>>>>>
>>>>>>>>>>> The limit is a very clear concept. S is not infinite and CANNOT be
>>>>>>>>>>> defined in ANY other way, except by its partial sums. If you think
>>>>>>>>>>> otherwise, then you would have to show me ALL of S. You can't.
>>>>>>>>>>>
>>>>>>>>>>> There is no S = S_inf. That's just nonsense.
>>>>>>>>>>>>
>>>>>>>>>>>> It is lim_n S_n = S.
>>>>>>>>>>> NO. Lim S is very well defined to be 1/3 in the case of 0.333...
>>>>>>>>>>>
>>>>>>>>>>> All you've had so far is hand waving and excuses which for the most
>>>>>>>>>>> part are not even relevant to the discussion. You are trying to
>>>>>>>>>>> distract from the main topic which is the FACT that Euler defined S
>>>>>>>>>>> = Lim S and moreover that it was a very big blunder!
>>>>>>>>>> S=lim_n S_n =1/3 Nope. S is a series. Lim_n S_n is the number 1/3.
>>>>>>>>>> Two totally different objects, therefore cannot be equal. =0.333...
>>>>>>>>>> if (S_n) is the sequence 0.3, 0.33, 0.333, ...
>>>>>>>>> Bullshit. S = 0.333.... Lim S = 1/3
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No contradictions here.
>>>>>>>>>
>>>>>>>>> Right, only your garbage.
>>>>>>>> S and lim_n S_n are the same object by definition.
>>>>>>> Changing your tune again?
>>>>>>>
>>>>>>> No. S and Lim_n S_n are two different things. Your ill-formed
>>>>>>> definitions (ala Euler S= Lim S) are irrelevant. LMAO.
>>>>>> They are exactly the same thing by definition.
>>>>>>
>>>>>> S := lim_n S_n.
>>>>> You just don' get it, do you? You cannot say that a <series> is equal to
>>>>> a <number> because they are two different objects. You're such a moron.
>>>> A series *is* a number,
>>> Nope. A series is not a number.
>>>
>>> "In mathematics, a series is, roughly speaking, a description of the
>>> operation of adding infinitely many quantities, one after the other, to a
>>> given starting quantity." - The wikipedia moronica
>>>
>>> In other words, it cannot ever be a number because "adding infinitely many
>>> quantities" is a dream, in other words a super task which is impossible.
>>> LMAO.
>>>
>>> Look idiot, Euler defined it this way S = Lim S:
>>>
>>> Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+...
>>> &c.
>>>
>>> Only the dumbest mainstream academics are still arguing.
>>>> or a function that gives numbers for every x.
>>> What?! LMAO.
>> A series is a number (or a function that gives numbers).
>
> No, idiot. NO.
>
>> For example, Taylor series takes real numbers x and gives out a real number.
>
> A Taylor series (which is hopelessly inferior to the Gabriel Polynomial)
> never produces anything but a rational number approximation.

måndag 30 augusti 2021 kl. 13:18:33 UTC+2 skrev Eram semper recta:
> 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 was a preeminent mainstream crank like most on this newsgroup.
I think you're deliberately misunderstanding what a series is.

On Monday, 30 August 2021 at 08:23:48 UTC-4, FromTheRafters wrote:
> Eram semper recta explained on 8/29/2021 :
> > On Sunday, 29 August 2021 at 10:12:02 UTC-4, markus...@gmail.com wrote:
> >> söndag 29 augusti 2021 kl. 02:24:50 UTC+2 skrev Eram semper recta:
> >>> On Saturday, 28 August 2021 at 12:07:02 UTC-4, markus...@gmail.com wrote:
> >>>> lördag 28 augusti 2021 kl. 18:03:31 UTC+2 skrev Eram semper recta:
> >>>>> On Saturday, 28 August 2021 at 12:01:31 UTC-4, markus...@gmail.com wrote:
> >>>>>> lördag 28 augusti 2021 kl. 14:49:19 UTC+2 skrev Eram semper recta:
> >>>>>>> On Friday, 27 August 2021 at 21:23:23 UTC-4, markus...@gmail.com wrote:
> >>>>>>>> fredag 27 augusti 2021 kl. 23:13:24 UTC+2 skrev Eram semper recta:
> >>>>>>>>> On Friday, 27 August 2021 at 16:52:17 UTC-4, markus...@gmail.com
> >>>>>>>>> wrote:
> >>>>>>>>>> torsdag 19 augusti 2021 kl. 15:45:07 UTC+2 skrev Eram semper recta:
> >>>>>>>>>>> On Wednesday, 18 August 2021 at 11:14:13 UTC-4, markus...@gmail.com
> >>>>>>>>>>> wrote:
> >>>>>>>>>>>> onsdag 18 augusti 2021 kl. 17:00:10 UTC+2 skrev Eram semper recta:
> >>>>>>>>>>>>> On Wednesday, 18 August 2021 at 10:53:34 UTC-4,
> >>>>>>>>>>>>> markus...@gmail.com wrote:
> >>>>>>>>>>>>>> onsdag 18 augusti 2021 kl. 06:30:54 UTC+2 skrev Eram semper
> >>>>>>>>>>>>>> recta:
> >>>>>>>>>>>>>>> On Tuesday, 17 August 2021 at 19:28:57 UTC-4,
> >>>>>>>>>>>>>>> markus...@gmail.com wrote:
> >>>>>>>>>>>>>>>> tisdag 17 augusti 2021 kl. 23:53:01 UTC+2 skrev Eram semper
> >>>>>>>>>>>>>>>> recta:
> >>>>>>>>>>>>>>>>> On Tuesday, 17 August 2021 at 03:35:11 UTC-4,
> >>>>>>>>>>>>>>>>> zelos...@gmail.com wrote:
> >>>>>>>>>>>>>>>>>>> It is a WELL-FORMED NAME, unlike the bullshit 0.333.... no,
> >>>>>>>>>>>>>>>>>>> it's name is Bob, we write it as 1/3 Well, if one builds
> >>>>>>>>>>>>>>>>>>> on shit, the end result is always shit.
> >>>>>>>>>>>>>>>>>> That is why everything you have is shit. But the cauchy
> >>>>>>>>>>>>>>>>>> constructions are valid and works fine.
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>>> You DO CARE!
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> I do not
> >>>>>>>>>>>>>>>>>>> You still obey S = Lim S.
> >>>>>>>>>>>>>>>>>> nope, again S=(0,0.1,0.11,0.111,0.1111,...)
> >>>>>>>>>>>>>>>>>> S=Lim S
> >>>>>>>>>>>>>>>>>> Substitute
> >>>>>>>>>>>>>>>>>> (0,0.1,0.11,0.111,0.1111,...)=Lim
> >>>>>>>>>>>>>>>>>> (0,0.1,0.11,0.111,0.1111,...)
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> Is pure nonsense.
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> What we have is S=lim S_n
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> HUGE difference.
> >>>>>>>>>>>>>>>>>>> Your student Markus Klyver recently admitted it - not that
> >>>>>>>>>>>>>>>>>>> it matters much because he is a moron just like you.
> >>>>>>>>>>>>>>>>>> He has admitted that S=lim S_n, not your shit.
> >>>>>>>>>>>>>>>>> S = Lim S_n is EXACTLY what is meant by S = Lim S.
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> Crank: One who cannot be convinced in the face of
> >>>>>>>>>>>>>>>>> overwhelming evidence.
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> Fits you and Klyver perfectly!
> >>>>>>>>>>>>>>>>>>> Of course what Euler wrote is of importance. Didn't you
> >>>>>>>>>>>>>>>>>>> just say "build on the same foundational ideas"? You
> >>>>>>>>>>>>>>>>>>> pathetic, stupid crank! The ideas he wrote is what
> >>>>>>>>>>>>>>>>>>> matters, if he miswrote somewhere is much less important.
> >>>>>>>>>>>>>>>>>>> You mean what YOU think matters. Chuckle. That is what
> >>>>>>>>>>>>>>>>>>> matters to the mathematical community, of which you are not
> >>>>>>>>>>>>>>>>>>> part. See, no answer because you know I am right!!!
> >>>>>>>>>>>>>>>>>> Ah so by not addressing most of the things I post to you,
> >>>>>>>>>>>>>>>>>> you admit here that I am right then.
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> Or are you gonna do cherry picking/be a hypocrite and say it
> >>>>>>>>>>>>>>>>>> is suddenly different for you?
> >>>>>>>>>>>>>>>> Why do you like to omit the subscript?
> >>>>>>>>>>>>>>>> S=lim S is bad notation since the right hand side depends on
> >>>>>>>>>>>>>>>> n, whereas the left hand side has no dependence on n.
> >>>>>>>>>>>>>>> The left hand side IS dependent on the right hand side. It is
> >>>>>>>>>>>>>>> the LIMIT of the series S. The limit is very much dependent on
> >>>>>>>>>>>>>>> n and also how it is realised in analysis.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> The series IS its nth partial sum. Nothing else.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> It's S=lim S_n.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> Grow a brain, you idiot! Suddenly you're worried about
> >>>>>>>>>>>>>>> notation? LMAO.
> >>>>>>>>>>>>>> The limit of the series (which is a constant) is the series
> >>>>>>>>>>>>>> itself, but that not how the series is defined.
> >>>>>>>>>>>>> Not at all. That is how you would like it to be, but the reality
> >>>>>>>>>>>>> is very different.
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> A series is NOT an infinite sum.
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> The series is defined as the limit of the partial sums S_n..
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> Hence S = lim_n S_n. Right. S = Lim S. No difference.
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> S = lim_n S is trivially the since S does not depend on n.
> >>>>>>>>>>>>> S very much depends on its partial sums defined by
> >>>>>>>>>>>>> S(n)=(1/3)[1-10^(-n)].
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> S is defined by its partial sums. There is no such thing as an
> >>>>>>>>>>>>> infinite S or even a unique S.
> >>>>>>>>>>>> S depends on its partial sums, but not on n.
> >>>>>>>>>>> Not quite correct. S depends on its nth partial sum as defined by
> >>>>>>>>>>> S(n)=(1/3)[1-10^(-n)]. Therefore, the limit itself depends on n
> >>>>>>>>>>> too, because the limit is realised by considering what happens as n
> >>>>>>>>>>> becomes very large.
> >>>>>>>>>>>
> >>>>>>>>>>> The limit is a very clear concept. S is not infinite and CANNOT be
> >>>>>>>>>>> defined in ANY other way, except by its partial sums. If you think
> >>>>>>>>>>> otherwise, then you would have to show me ALL of S. You can't..
> >>>>>>>>>>>
> >>>>>>>>>>> There is no S = S_inf. That's just nonsense.
> >>>>>>>>>>>>
> >>>>>>>>>>>> It is lim_n S_n = S.
> >>>>>>>>>>> NO. Lim S is very well defined to be 1/3 in the case of 0.333....
> >>>>>>>>>>>
> >>>>>>>>>>> All you've had so far is hand waving and excuses which for the most
> >>>>>>>>>>> part are not even relevant to the discussion. You are trying to
> >>>>>>>>>>> distract from the main topic which is the FACT that Euler defined S
> >>>>>>>>>>> = Lim S and moreover that it was a very big blunder!
> >>>>>>>>>> S=lim_n S_n =1/3 Nope. S is a series. Lim_n S_n is the number 1/3.
> >>>>>>>>>> Two totally different objects, therefore cannot be equal. =0..333...
> >>>>>>>>>> if (S_n) is the sequence 0.3, 0.33, 0.333, ...
> >>>>>>>>> Bullshit. S = 0.333.... Lim S = 1/3
> >>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>> No contradictions here.
> >>>>>>>>>
> >>>>>>>>> Right, only your garbage.
> >>>>>>>> S and lim_n S_n are the same object by definition.
> >>>>>>> Changing your tune again?
> >>>>>>>
> >>>>>>> No. S and Lim_n S_n are two different things. Your ill-formed
> >>>>>>> definitions (ala Euler S= Lim S) are irrelevant. LMAO.
> >>>>>> They are exactly the same thing by definition.
> >>>>>>
> >>>>>> S := lim_n S_n.
> >>>>> You just don' get it, do you? You cannot say that a <series> is equal to
> >>>>> a <number> because they are two different objects. You're such a moron.
> >>>> A series *is* a number,
> >>> Nope. A series is not a number.
> >>>
> >>> "In mathematics, a series is, roughly speaking, a description of the
> >>> operation of adding infinitely many quantities, one after the other, to a
> >>> given starting quantity." - The wikipedia moronica
> >>>
> >>> In other words, it cannot ever be a number because "adding infinitely many
> >>> quantities" is a dream, in other words a super task which is impossible.
> >>> LMAO.
> >>>
> >>> Look idiot, Euler defined it this way S = Lim S:
> >>>
> >>> Daher ist uns Bruch 1/(1+a) gleich dieser unendlichen Reihe 1-a+aa-aaa+...
> >>> &c.
> >>>
> >>> Only the dumbest mainstream academics are still arguing.
> >>>> or a function that gives numbers for every x.
> >>> What?! LMAO.
> >> A series is a number (or a function that gives numbers).
> >
> > No, idiot. NO.
> >
> >> For example, Taylor series takes real numbers x and gives out a real number.
> >
> > A Taylor series (which is hopelessly inferior to the Gabriel Polynomial)
> > never produces anything but a rational number approximation.