/sci/ - Science & Math

[Anonymous No.10750346]

FUCK MATHS

[Anonymous No.10750358]

>>10750346
2+2=4 quick mafs

[Anonymous No.10750367]

>>10750346
Accept only numberphile ever claimed the bottom one to be true, and all actual mathematicians recognize this to be a divergent sum. Btw, saying either sum "equals infinity" is also technically wrong. They diverge.

[Anonymous No.10750375]

>>10750367
wtf ikr the -1/12 meme got DEBUNKED a long time ago why do brainlets keep pushing it???

[Anonymous No.10750379]

>>10750367
I won't accept it because I also claimed it's true.
still do

[Anonymous No.10750382]

>>10750379
That doesnt make any goddamn sense

[Anonymous No.10750385]

>>10750382
accept it, kiddo

[Anonymous No.10750386]

>>10750375
Because brainlets dont know what analytic continuation is or how it is different from saying a sum equals something

[Anonymous No.10750650]

>>10750386
How do you feel about non-integer dimensions then?

[Anonymous No.10750675]

>>10750375
It's a meme on /sci/.

[Anonymous No.10750681]

>>10750650
Its almost like the word is being used to represent two separate ideas

[Anonymous No.10750688]

>>10750650
Dimensions of a vector space have nothing to do what what you just posted

[Anonymous No.10750710]

>>10750681
>>10750688
So why are fractal's fine but 2-adic numbers aren't?

[Anonymous No.10750715]

>>10750710
What the FUCK are you talking about

[Anonymous No.10750719]

>>10750715
Read the thread and reflect.

[Anonymous No.10750725]

>>10750715
https://youtu.be/XFDM1ip5HdU?t=9m

[Anonymous No.10752460]

>>10750346
I'm more puzzled about the first one than the -1/12 meme.

[Anonymous No.10752484]

>>10752460
1/3 + 1/4 > 0.5
1/5+...+1/8 > 0.5
1/9+...+1/16 > 0.5
etc.

[Anonymous No.10752517]

>>10750367
numberphile lost crediblity with that vid.
It was a wild assertion dropping the Reimann Hypothesis with shit evidence. basically, "trust me, it's -1/12 because i'm a math professor"

provided shit context.

[Anonymous No.10753440]

>>10752484
1/9+1/16=.17636111111...<.5
Wtf are you talking about

[Anonymous No.10753446]

>>10750375
>>10750386
>>10750367
have you ever saw that quantum mechanic videos in youtube? they are full of bullshit also easily proven wrong

[Anonymous No.10753453]

>>10753440
lrn2read

[Anonymous No.10753456]

>>10750367
>Btw, saying either sum "equals infinity" is also technically wrong
Wrong
>>10750375
Because thermodynamics and memes

[Anonymous No.10753460]

>>10753453
So sorry

[Anonymous No.10753463]

>>10753440
wow imagine being so retarded he clearly meant pic related

[Anonymous No.10753467]

>>10753440
http://mathforum.org/library/drmath/view/56918.html
Scroll to the bottom of that page. He didn't mean 1/9+1/16, he meant 1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16

[Anonymous No.10753482]

>>10752484
>1/3 + 1/4 > 0.5
>1/5+...+1/8 > 0.5
>1/9+...+1/16 > 0.5
wtf prove? why not just use that french or german guy name theorem using integrals?

[Anonymous No.10753495]

>>10753463
[math] \displaystyle
\sum_{i=9}^{16} \dfrac{1}{i}
[/math]
Optimized.

[Anonymous No.10753657]

>>10753495
based

[Anonymous No.10753798]

>>10753495
Has science gone too far?

[Anonymous No.10753805]

>>10750650
ask your mother about my cock curve

[Anonymous No.10753816]

>>10750367
What's a divergent sum?

[Anonymous No.10753822]

>>10753816
explodes to infinity

[Anonymous No.10753834]

>>10753822
So what's the real reason for 1+2+3+4.....= -1/12 ?
Also has it been disproved?
Math noob here

[Anonymous No.10753839]

>>10753834
The Riemann zeta function can be "extended" into the domain of negative numbers. Plugging in -1 into the Riemann Zeta function yields -1/12 which also happens to be equal to 1+2+3+4+5+...

It's known as analytic continuation and it's not a "real" equality.

[Anonymous No.10753860]

>>10753834
https://youtu.be/sD0NjbwqlYw?t=10m

[Anonymous No.10753872]

>>10753834
It's easy to confuse yourself with this shit but it's quite simple.

All that the ramanujan summation stuff, cutoff and zeta regularization does, is look at the smoothed curve at x = 0.
What sums usually do is look at the value as x->inf.

It's just a unique value you can assign to a sum, really they have many such values.

https://en.wikipedia.org/wiki/File:Sum1234Summary.svg

[math] \displaystyle
\zeta \neq \Sigma
[/math]

[Anonymous No.10753878]

>>10753839
Hmm, I don't think I'm at a level yet where I can underwhelming what analytic continuation is , but thanks for the help .
Also for anyone's who is still confused, this article is nice:
https://plus.maths.org/content/infinity-or-just-112

[Anonymous No.10753909]

>>10753878
>what analytic continuation is
angle-preserving

[Anonymous No.10754003]

>>10750367
He asked physicists, and yes they are always doing that sort of bs.

[Anonymous No.10754033]

>>10750367
>>10750375
>>10750386
>>10754003
It's true you fucking faggots. A series failing to converge conditionally doesn't preclude it from having a sum any more than a series failing to converge absolutely precludes it from having a sum or a rational series failing to converge in the rationals precludes it from having a sum.

[Anonymous No.10754049]

>>10750346
>>10754033
PS: You can regularize the harmonic series also, and it sums to the Euler-Mascheroni constant.

[Anonymous No.10754064]

Hard to believe so many retards keep saying NUH UH IT DOESN'T EQUAL -1/12 BECAUSE I'M A DUMB BRAINLET AND MY BRAIN IS TOO STUPID TO COMPREHEND IT and also NUMBERPHILE BAD. Fucking kill yourselves idiots.

[Anonymous No.10754315]

>>10754033
>>10754049
>>10754064
Buttmad physicists detected. Sorry to tell you but whatever they told you is a meme because they think you cannot grasp basic analysis.

[Anonymous No.10754321]

>>10754315
>t. doesn't know what regularization is
>t. doesn't know what analytic continuation is
Fuck off back to your calc 1 class

[Anonymous No.10754325]

>>10754315
>Buttmad
You must be 18 years or older to post here

[Anonymous No.10754330]

>>10754321
I know both, and if you knew either, you would understand why it still makes absolutely no sense to say it "has a sum". You are defining a whole new function.
>>10754325
Or are you butt-frustrated?

[Anonymous No.10754374]

>>10754330
>You are defining a whole new function.
Let's see: Do you give it a "whole new name" when you extend addition of naturals to addition of integers? Addition of integers to addition of rationals? Addition of rationals to addition of reals? Addition of reals to addition of complex numbers? Ordinary addition to limits of partial sums? The Leibniz series because it's not convergent in the rationals? Conditionally convergent series because they can be rearranged to yield any value, unlike "ordinary" addition?

No, you're just being a massive, tremendously stupid faggot.

[Anonymous No.10754431]

I must be retarded, how do you prove that the top diverges?

I know you usually prove divergence by proving that the sum is always above 1/n, so how do you prove it for 1/n?
I used to know this

[Anonymous No.10754436]

>>10754431
Group the summands in groups of 1, 2, 4, 8, and so on consecutively, then do a comparison test with a series that can easily be seen to diverge.

[Anonymous No.10754495]

>>10754374
see >>10753860
and realize u r a retard

[Anonymous No.10754505]

>>10754431
>I must be retarded,
lrn2read
>>10752484

[Anonymous No.10754506]

>>10754495
That video supports my point you braindead mongoloid. I already mentioned analytic continuation you illiterate bag of shit.

[Anonymous No.10754519]

>>10753834
It hasn't been "disproved", there's just a bunch of dumb faggots saying THAZZ NOT REAL SUMMATION :DDD as if we needed to create a new name every time we extended summation to a new context, see >>10754374.

[Anonymous No.10754554]

>>10754505
how does that prove anything? The number of terms in the sum gets longer each time

[Anonymous No.10754555]

>>10754374
Well you would be right if the continuation of the dirichlet series was in any fucking sense an extension of addition. Analytic continuation is a broad whose concepts have nothing to do with "sums". The point is to exentd already analytic functionw defined in an open set on a bigget set of the complex plane. If you want to see actual methods for extending "sums" look up ramanujans method. You know jack shit about complex analysis.

[Anonymous No.10754557]

>>10753834
>Also has it been disproved?
>Math noob here
That isn't how math works sweetie

[Anonymous No.10754559]

>>10754554
ok I think I get it now

[Anonymous No.10754560]

>>10754555
Broad technique*

[Anonymous No.10754607]

>>10754506
triggered.
so easy

[Anonymous No.10754612]

>>10754555
>You know jack shit about complex analysis.
I clearly know much more than you, you braindead sack of shit.
>Analytic continuation is a broad whose concepts have nothing to do with "sums".
The point is that analytic continuation IS HOW YOU CAN NATURALLY DEFINE A NEW CLASS OF SUMS YOU FUCKING IDIOT. This is like saying "limits have nothing to do with sums" (limit of partial sums definition) or "Cauchy-completeness has nothing to do with sums" (irrational sums of rational series).
>If you want to see actual methods for extending "sums" look up ramanujans method.
You... you fucking mongoloid. Ramanujan summation also sums divergent series. You're BTFO'ing yourself and you don't even realize it. Wew.

[Anonymous No.10754616]

>>10754607
Fuck off, retard

[Anonymous No.10754618]

>>10754555
>the continuation of the dirichlet series was in any fucking sense an extension of addition
it literally is tho

[Anonymous No.10754622]

>>10754612
https://en.m.wikipedia.org/wiki/Analytic_continuation Why people spout wrong shit when everything is a google away.
>b...but muh wikipedia
Then check Conways complex analysis. And yes I was putting Ramanujans method as an example where you incoherent babble could barley make sense.

[Anonymous No.10754633]

>>10754622
What the fuck was your point in linking to the Wikipedia article on analytic continuation? Are you fucking stupid? What did I say that was wrong, you dumb shit?
>I was putting Ramanujans method as an example where you incoherent babble could barley make sense
There's a whole field of study on divergent series you literal retard.
https://en.wikipedia.org/wiki/Divergent_series
Seriously, stop embarrassing yourself.

[Anonymous No.10754634]

>>10754616
seething

[Anonymous No.10754637]

>>10754634
cope

[Anonymous No.10754644]

>>10754618
How in the name of fuck it is? What does rieman functional equation has to do with addition? Yes it exentds in a unique way a complex meromorphic function defined in a semiplane as a convergent series, but there's literally nothing resembeling "series" in the rest of the plane.
>>10754633
Well you could point me where in the article or any fucking book on complex analysis does it say that the point of "analytic continuation is to extend sums" you absolute retardard. It literally is just finding ways to extend functions defines in some ways. Are you confused because analytic functions can be expanded through power series? You sound like a schizo babbaling nonsense.

[Anonymous No.10754653]

>>10754633
>There's a whole field of study on divergent series
Yea it's called introductory real analysis. You are a brainlet undergrad, who knows so little you cannot understand your own retardation.

[Anonymous No.10754658]

>>10754644
>it exentds in a unique way
There's your answer.
>there's literally nothing resembeling "series" in the rest of the plane
This is like saying "there's literally nothing resembling addition in a limit". The fact that you lack imagination or understanding is not proof of anything.
>the point of "analytic continuation is to extend sums"
I didn't say the point of analytic continuation is to extend sums you illiterate baboon. I said analytic continuation is A WAY you can extend sums. Is that too hard for your pea brain to understand?
>You sound like a schizo babbaling nonsense.
Yeah, I'm sure all the mathematicians who work on divergent series are schizos and you're the one who's totally sane. Sure kid.

You're out of your depth here. Go back to your basic calculus class.

[Anonymous No.10754661]

>>10754653
So you admit divergent series are mathematically valid? Kek, nice of you to finally admit it.
>You are a brainlet undergrad
Stop projecting your own lack of education on to me. There's no need to continue exposing your ignorance and embarrassing yourself.

[Anonymous No.10754666]

>>10754637
laughter is very relaxing, ty

[Anonymous No.10754672]

>>10754644
>Well you could point me where in the article or any fucking book on complex analysis does it say that the point of "analytic continuation is to extend sums"
https://en.wikipedia.org/wiki/Analytic_continuation
second sentence of the article: Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.

[Anonymous No.10754684]

>>10754555
>>10754644
you're saying all of these are schizo nonsense? :O
https://en.wikipedia.org/wiki/Ces%C3%A0ro_summation
https://en.wikipedia.org/wiki/Borel_summation
https://en.wikipedia.org/wiki/H%C3%B6lder_summation
https://en.wikipedia.org/wiki/Lambert_summation

[Anonymous No.10754689]

>>10754658
>>10754661
I think I'm mixing up your arguments. So generically, you are both retarded. But one of you is just ranting about calling something a sum which is absolutely retarded and the other is far more lost. Just a few things. No fucking mathematician worth its salt would call the riemann zeta function an extended sum. It's an extension of a function that is defined as an infinite series. Woopty fucking doo. Calling it and extended sum is just a laughably bad description of the actual process. Also
>>10754612
>The point is that analytic continuation IS HOW YOU CAN NATURALLY DEFINE A NEW CLASS OF SUMS
No it's not. A sum is a fucking operation, continuation is nothing limits exist and you can define a function in a certain way at those points and analytic continuation is much more used with shit like multivalued functions and riemann surfaces which have nothing to do with "sums"
>>10754672
Yes no fucking shit sherlock, the technique is far broader than just that and that's the point. Read the first sentence.

And for the record infinite series are considered sums, because they literally are constructed through repeated addition and because they share PLENTY of properties with usual addition. The Riemann zeta function doesn't even admit this kind analysis because it's not an operation, IT'S A FUCKING MEROMORPHIC FUNCTION THAT HAPPENS TO REDUCE TO THE DIRICHLET SERIES IN SOME PARTS OF THE PLANE. This has to be one of the most retarded arguments I've been recently. If you want to keep using the notation for the series even off the half plane where it makes sense, be my guest, it changes nothing.

[Anonymous No.10754691]

>>10754689
You're a fucking dumbass. Then why are all of these called summation methods, by mathematicians?
>>10754684

[Anonymous No.10754693]

>>10754689
>the technique is far broader than just that
Nobody said it was "just that" you lying piece of shit.

[Anonymous No.10754697]

>>10754684
>>10754691

Jesus fucking christ. I'm not denying that fucking regularization techniques exist, but that calling the riemann zeta function, or for that matter, analytic continuation as a whole "extending sums" is retarded as analytic continuation is a much broader concept that rises in cases where a sum is not even fucking present. Jesus, Zeta function regularization isn't even the most common in applications. Most of it is about applications to number theory.

[Anonymous No.10754698]

>>10754689
>A sum is a fucking operation, continuation is nothing limits exist and you can define a function in a certain way at those points
How about you write a grammatically-coherent sentence instead of blathering like the idiot you are?

[Anonymous No.10754700]

>>10754693
The big retards here are claiming that the riemann zeta function is a way to extend sums whatever the fuck that means. It's a way to extend a function.

[Anonymous No.10754701]

>>10754698
Oh no whatever will I do now.

[Anonymous No.10754702]

>>10754689
>The Riemann zeta function doesn't even admit this kind analysis because it's not an operation
A function is an operation too you fucking dolt.
https://en.wikipedia.org/wiki/Operation_(mathematics)#Definition
And zeta function regularization IS ONE KIND OF SUMMATION METHOD YOU FUCKING RETARD HOLY SHIT.
https://en.wikipedia.org/wiki/Category:Summability_methods

[Anonymous No.10754705]

>>10754689
>If you want to keep using the notation for the series
So do you keep changing notation between natural number addition, rational number addition, real number addition, complex number addition, cardinal addition, ordinal addition, hyperreal addition, surreal addition, conditionally convergent series, absolutely convergent series, and so on? No, because only a dumbass would do that, right? Well, that's you.

[Anonymous No.10754707]

>>10754702
Yes it's a sumability method as it extends something defined as a series. It's not a fucking sum. And if you weren't such an autistic, retarded piece of shit you would understand that operation usually means above 1nary operations.

[Anonymous No.10754711]

>>10754700
>The big retards here are claiming that the riemann zeta function is a way to extend sums
Analytic continuation is a way to assign values to divergent sums, i.e. extend summation beyond the limit-of-partial-sums definition. Are you contesting this basic fact? I honestly can't even tell what you're getting at anymore.

[Anonymous No.10754712]

>>10754705
Well, then why do almost all fucking texts use a xi for the riemann zeta function?

[Anonymous No.10754713]

>>10754697
>analytic continuation is a much broader concept that rises in cases where a sum is not even fucking present
Oh. My. God. You are actually braindead.

Limits arise in contexts where "a sum is not even fucking present". So you're saying that the limit-of-partial-sums definition of infinite series is retarded? You dense motherfucker.

[Anonymous No.10754717]

>>10754697
>Most of it is about applications to number theory.
It's used plenty in physics not just number theory you ignorant fool.

[Anonymous No.10754719]

>>10754711
Read this
>>10754705
I suppose it's one retarded using "sum" meaning literally addition and thinking the riemann zeta function is addition on some new number system or whatever the fuck. And a bunch of autists screaming because they use "sum" to mean divergent series. If everyone could actually read the posts, they would understand I'm just talking about the retarded notion that the rieman zeta function is a new kind of addition and we shouldn't chagne notation.

[Anonymous No.10754722]

>>10754712
>why do almost all fucking texts use a xi for the riemann zeta function
>xi
>zeta function
>zeta
AHAHAAHAHAHAHAAHAHAHAHAHAHAAHAHAA YOU FUCKING MORON you have no idea what you're talking about do you

[Anonymous No.10754726]

>>10754707
>It's not a fucking sum.
It is a "fucking sum" hence
https://en.wikipedia.org/wiki/Divergent_series
https://en.wikipedia.org/wiki/Category:Summability_methods

[Anonymous No.10754727]

>>10754707
>operation usually means above 1nary operations
Who said *summation* is an unary operation? The *zeta function* itself is unary, the summation method based on it isn't. Jesus christ, I swear you get dumber by the minute.

[Anonymous No.10754729]

>>10754719
>the rieman zeta function is a new kind of addition
No one (except perhaps in your schizo brain) said the zeta function is a new kind of addition. What I said was that zeta function *regularization* is a kind of addition, that is, an extension of the limit-of-partial-sums definition.

[Anonymous No.10754732]

>>10754717
Well at least I understand the meaning of the words "most" and "all.
>>10754713
Do you have any idea how the Riemann Zeta is actually defined? Also no I'm talking in particular ABOUT THE RIEMANN ZETA FUNCTION, so I'm not sayinng anythinf remotely similar to your babble as the riemann zeta function is jot defined in any way like thay, and that's the whole point. The limit of partial sums STILL CONTAINS PARTIAL SUMS IN THE DEFINITION. Check out Riemanns functional equation and I dare you to tell me what in actual fuck does that have to do with addition.
>>10754722
Well it looks similar lmao, but you see how it still shows no one uses the "series" representation.
>>10754726
>>10754729
Check this for the love of god.
>>10754705

[Anonymous No.10754735]

>>10754729
No it's not an extension of that. ITS DEFINED THROUGH THE RIEMAMM FUNCTIONAL EQUATION.

[Anonymous No.10754737]

What the fuck are you even arguing about retards. The Dirichlet series is only A WAY to compute Zeta function for Re(s) >1. Just like sinx you can compute through geometry for real x but complex sine function is much broader. Historically series appeared earlier but that doesn’t mean that zeta function is related to series for all s.

[Anonymous No.10754740]

>>10754737
It's a discussion if the riemann zeta function deserves to be called an extended sum or whatever. It's pretty fucking retarded.

[Anonymous No.10754741]

>>10754732
"Most" is wrong here you braindead idiot.
>Check out Riemanns functional equation and I dare you to tell me what in actual fuck does that have to do with addition.
The functional equation is not how the Riemann zeta function is defined you dolt. The Riemann zeta function was first defined by Euler THROUGH ITS SERIES DEFINITION.
>Well it looks similar lmao
Hahaha, not only are you stupid but you also have visual impairment. That explains the low quality of your posts and reading comprehension.
>no one uses the "series" representation
The series representation is the whole starting point and basis on which the zeta function is introduced, you shitbag.

[Anonymous No.10754743]

>>10754735
THE RIEMANN FUNCTIONAL EQUATION IS A DERIVED IDENTITY, NOT A DEFINITION YOU STUPID IDIOT.

[Anonymous No.10754749]

>>10754743
>retard is arguing about things he don’t understand
Dumbass, Riemann Zeta function is the function that satisfies Riemann functional equation. It is definition, idiot.

[Anonymous No.10754754]

>>10754689
>>10754697
>>10754700
>>10754707
>>10754719
>>10754732
>We shall be concerned throughout with methods of summability consistent with the method of analytic continuation.
Literally the first sentence of https://msp.org/pjm/1952/2-2/pjm-v2-n2-p04-p.pdf.. Analytic continuation IS A METHOD OF SUMMABILITY.

Now go fucking kill yourself you braindead, useless sack of dogshit.

[Anonymous No.10754755]

>>10754749
You are so incredibly, incomprehensibly dumb. Just because a function satisfies a function equation doesn't mean the definition of that function IS that functional equation.

[Anonymous No.10754757]

>>10754741
>The Riemann zeta function was first defined by Euler THROUGH ITS SERIES DEFINITION
Yes the historic construction of the function began with the dirichlet series and attampts to extend it. The functional equation is ONE WAY TO EXTEND THE FUNCTION TO THE REST OF THE PLANE. Not even the Gamma function identity is enough. Granted there are other definitions but the functional equation is pretty standard. As you said you fiest derive the identity, but you then realize that the identity works for an even larger set of numbers so you use this fact to extend the definition and so a really easy way to define it is through that functional equation.

[Anonymous No.10754763]

>>10754757
Conclusion: You can use the zeta function to find sums for a certain class of divergent series (namely those of the form n^s).

And KEEP IN MIND zeta function regularization IS NOT THE ONLY WAY to get those same values.

[Anonymous No.10754764]

>>10754754
>IT HAS SUM ON IT'S NAME STOP THE FUCKING PRESS
Yes you had a function that was definad through a series and you extended it to other parts of the complex plane. It's still not a fucking sum.
>>10754755
No but it's a way to define it you shitbag.

[Anonymous No.10754768]

>>10754764
>literally all professional mathematicians in the field call it a sum
>N-N-NOOOOOOOO IT'S NOT A SUM BECAUSE I, AN ANONYMOUS GENIUS POSTER ON THE SCIENTIFIC FORUM KNOWN AS 4CHANNEL, KNOW MUCH BETTER THAN THEY DO

[Anonymous No.10754769]

>>10754755
Functions can be defined through functional equations, like gamma function. Educate yourself, idiot.

[Anonymous No.10754774]

>>10754768
>literally all professional mathematicians in the field call it a sum
Who?

[Anonymous No.10754775]

>>10754764
>Ok I admit you were right in saying that the zeta function was defined in terms of the series.
>BUT HEY! I'll take this functional identity derived from said definition, claim it's the definition instead, and therefore claim it was *not* defined in terms of the series!
Solid reasoning right there. Simply spectacular.

[Anonymous No.10754779]

>>10754774
Are you blind? All professional mathematicians in the field call it a sum. Analytic continuation a summability method. Do you know what that is? Holy shit.

[Anonymous No.10754782]

>>10754763
Well that only makes sense if you think those divergent series have any meaning at all. Yes I understand in many problems people need to regularize divergent sums but it's not pedantic to be cautious about the languange you are using. At least in mathematics.
>>10754768
You don't understand what the hell a sumability method is and there's nothing that outs you better as ignorant retard when you resort to using the literal name of things.
>>10754775
Lmao now I'm absolutely sure you have no idea what analytic continuation actually is.

[Anonymous No.10754784]

>>10754769
The functional equation for the gamma function doesn't even fix the function uniquely you stupid retard!

[Anonymous No.10754787]

>>10754782
>that only makes sense if you think those divergent series have any meaning at all
Yeah I'm sure all those mathematicians and all those articles and all those research papers are referring to something meaningless. Clearly.
>You don't understand what the hell a sumability method is
How so?
>Lmao now I'm absolutely sure you have no idea what analytic continuation actually is.
How so?

[Anonymous No.10754788]

>>10754784
Well, it does for the riemanm zeta function.

[Anonymous No.10754792]

>>10754754
>Analytic continuation IS A METHOD OF SUMMABILITY.
Yes, when sum exists. When you have a series and you know it converges you can use various methods to find the sum. But not when series diverges. You simply just to stupid to understand it.
Also analytic continuation is not only for sums. Gamma function has analytic continuations that doesn’t include series at all.

[Anonymous No.10754794]

>>10754788
Lol, thanks for making it perfectly clear you don't know what you're talking about. That relation only relates the values at $s$ to those at $1-s$. It doesn't fix the function, let alone define it.

Now fuck off.

[Anonymous No.10754802]

>>10754792
>But not when series diverges.
Read out the title of the linked article for me. Go on, read it out.

[Anonymous No.10754804]

>>10754792
>analytic continuation is not only for sums
Umm... who said it was "only for sums"?

[Anonymous No.10754809]

>>10754792
>Analytic continuation IS A METHOD OF SUMMABILITY.
>Yes
>But not when series diverges.
anon, analytic continuation is used to sum divergent series

[Anonymous No.10754822]

>>10754804
jews use it too, sometimes even three

[Anonymous No.10755562]

>>10754782
>You don't understand what the hell a sumability method is
A summability method is a method for summing divergent series.

[Anonymous No.10755969]

>>10755562
>summing
No

[Anonymous No.10756031]

>>10755562
Yes.

[Anonymous No.10756032]

>>10755969
https://www.encyclopediaofmath.org/index.php/Summation_methods
>Methods for constructing generalized sums of series, generalized limits of sequences, and values of improper integrals.

[Anonymous No.10756035]

>>10755969
>summation method
>not summing

[Anonymous No.10756055]

[math]S=\sum\limits_{n=0}^\infty 2^n = 1 + \sum\limits_{n=1}^\infty 2^n = 1 + 2\sum\limits_{n=0}^\infty 2^n = 1 + 2S[/math]
[math]S - 2S =1[/math]
[math]S= -1[/math]

[Anonymous No.10756088]

>>10756055
S=inf
inf-2*inf undefined
S=inf