/sci/ - Science & Math

>>6289404

This is kind of the reason I hate dealing with infinity pretty much anywhere. Such a poorly defined concept and it is abused by way too many incorrectly

>implying mathematicians are any better

>oh no, I can't solve equation ;(
>haha, let's make up an "imaginary" number

Was it Leonard Susskind?

>>6289420
xDD epic troll bro

>lim 1/x as x -> 0 = infinity

Wut i thought this was true?

>>6289649
different limit from the right and left (pos inf vs neg inf)

>>6289657
Ah right. Thanks.

Please remember its the THEORETICAL physicist that are the ass pies.
-Real Physicists

>>6289667
>-Real Physicists
"Real"

I would like to see you going into the woods and make actual physics.

Fucktard!

>>6289670
How is the 8th grade?

>>6289404
Could you link this talk? Does he have any papers published on this? I figure the video was probably ultra dumbed down. It's very often required in physics to regularize divergent integrals/expressions through analytic continuation (i.e. appealing to distribution theory), so most likely this is an example of that but maybe ultra-simplified to appeal to non-mathematicians.
Anyways, in the extended complex plane the limit's correct, but the guy sounds like a crackpot.

>He then proceeds to show that the important part is the -1/12 part and because we have two elementary strings, the number of dimensions is therefore 2*12+2 (time) = 26.

pretty sure I've seeen my professor did this before

also protip : The earlier term for theoretical physics is Mathematical physics. Thats right mathematicians are the cancer killing physics

>>6289425

OP here… yes, yes it was. Lecture 5 on YT.

>>6289742
I'm on the phone right now but see my sentence above. Can't miss it.

Also, I have this picture saved from the most widely used String Theory textbook (this book is a recommended textbook at MIT).

>>6289404
>says that:
>limx!01x=1
>is true (it's not)

Chemist here, can you elaborate on this? I've taken a fair number of mathematics courses but I don't see why this wouldn't be true.

>>6289756
OP here… it's a two-sided limit, hence it doesn't exist.

\lim_{x\rightarrow 0}{\frac {1}{x}} =\infty

Engineer here

this is what we've been taught all the time

>>6289404
as a statfag and someone who has not taken very theoretical math classes, what is the point of making the assertion that the sum of all positive integers is -1/12?

>>6289759
In fact, it's <span class="math"> \lim_{x\rightarrow 0^+}{\frac {1}{x}} =\infty [/spoiler] as OP previously stated because the limit is two sided or something like that. So, it's like half true.

As for the whole sum thing, it's not totally out of nowhere. What I mean is that if the serie was to converge the answer would be -1/12, so it kinda make some sense in a way, but I get your frustration OP. Also, know that string theory is pretty much the laughing stock of most physicists, because it's unprovable experimentally. Although I have to say it leads to pretty interesting results, I don't think it has to be taken too seriously. It's popular because it makes good pop sci and if it were to be true, it would lead to the understanding of the whole universe. Maybe the model of the strings could be use in other models (in fact, I think it is), I don't think the fundamental strings thingey should be taken too seriously doe.

Also, I hope that you understand what I'm trying to say, English isn't exactly my first language.

>>6289769
It's to know what the sum of all harmonics of strings is, because you know, string theory is pretty much based on the fact that everything is made up of fundamental strings.

trolling, I believe? Riemann zeta function regularization:

<span class="math">sum_{n=1}^\infty n/n^s=\zeta(s-1)[/spoiler]

take the limit as <span class="math">s\rightarrow 0[/spoiler]

<span class="math">\zeta(-1)=-1/12[/spoiler].

Isn't this like the 5th thread we've had about this in the last 3 days?

>>6289784

n=1n=−112

>>6289758
That's an interesting point. I know infinity isn't a number, you can't do algebra on it, etc, but I never thought about how to define it.

So the limit as x approaches 0 is divergent, but saying it's infinity isn't proper?

>>6289784
Indeed it is, just because of the Numberphile video (which was okay I think, but the extra with the zeta function was way better at explaning this). I believe it is another proof that this board is full of high schoolers who barelly know maths and physics, I mean it isn't like it's a new thing or anything. It's at the beggining of any book about string theory.

>>6289788
Not that guy, but yes exactly. The limit doesn't give the same answer if you take it one way or the other. Pic related, just to show you the limit and the graphic of the function.

>>6289800
Forgot pic

leonard actually did a good job explaining it
did you watch the other videos

Maybe I'm just mathematically retarded. The farthest I've gone is Calc 2.

Just a regular sum of positive integers results in a negative number? I don't understand how this is possible.

>>6289802
I'm having MAPLE flashbacks. It has seriously been a while since I've done any pure math.

I appreciate the visual. Crazy that a physicist would make this mistake in his research area. Being away from any real math other than for analysis of my completely experimental work I would probably have believed him at a glance. The approach of the limit from the positive side seems so intuitive I didn't consider the other.

When some retarded teacher introduced me to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>>6289788
No, the limit just doesn't exist by definition of a limit.

>>6289820
Infinity is unintuitive.

>>6289846

If you want to trash talk a system that has predictive applications in science and industry you might want to offer an alternative

5/10 because I replied

>>6289820
>Just a regular sum of positive integers results in a negative number? I don't understand how this is possible.


it isn't. they're either treating divergent series as convergent ones (which produces nonsensical results like -1/12) or they're pulling the limit bullshit in OP's post. both of the attempts at a proof are flawed and illogical.

>>6289839
I don't understand how people can make a signature that looks exactly like a scribble.

>>6289839
It's not really a mistake, because it is intensional. I mean, physicists mostly do those kind of things because it simplifies the whole calculation and in most case it is true in real life. Physicists tend to be lazy when doing maths, so they tend to do approximations and things like that.

>>6289848
This.

Look up the Epsilon-Delta (or sequential, equivalently) definition of the limit.

Infinity as a limit does not exist, unless we are on the extended real line, with a point at -infinity and +infinity, and the arctan distance, or other similar formulations of dealing with limits being infinity.

>>6289879
OP here… correct.

What Susskind is doing is nothing more than dividing by zero.

https://en.wikipedia.org/wiki/Division_by_zero#Formal_operations

And as even a HS student knows, once you start dividing by zero, you can prove anything since it's all meaningless after you've divided by zero.

So it's no wonder that you can get results like the ones we've discussed.

>>6289894
Eh, I'd have to look at it a bit longer...but if there truly is a cancellation factor in the action...it seems to be a legitimate regularization. Old school theoretical physicists seem to prefer multiplication by an exponential factor/parameter differentiation when they justify their analytic extensions, but as mentioned you can use the zeta function and it's perfectly fine. Ever wonder how they defined stuff like the Gamma function for negative complex values? It's a similar process.

You run into lots of divergent expressions in high level physics, there are plenty of rigorous mathematics to justify regularization of such expressions and their interpretations. This kind of renormalization is well known, documented, and rigorously constructed.

>mathematician calling analytic continuation nonsense
Confirmed for bait. Why is this thread so long? Is everyone just indulging in their inner autist today?

Isn't String Theory a bunch of bullshit anyway?

>>6289404
goddamn physicists are fucking halfwits.

>>6289994
yes it is...

>>6289790
>this board is full of high schoolers
Oh crap, all those boobie pictures weren't from world champ mathematicians?

>>6289894
If you really followed his lession, he didn't,

>>6289404
>community college tier

Knew you were full of shit the minute you started spouting memes.

Jesus fuck this thread is so idiotic, there are so many retarded statements.
They are not wrong, but completely out of context

I love it when people claim that the -1/12 is somehow a thing in string theory. doing it gives away the fact that these people learn their math and physics from youtube vids and don't actually know that its used in QFT and statistical mechanics ass well, and that there are rigorous mathematics that you can use to get -1/12 too.

i hate youtube popmath/sci, but it does an excellent job of exposing these retards who like to pretend to be intelligent like OP. (although susskinds lectures isnt completely popsci since he does at least touch on the actual physics and math)

>>6289404
A shitty YT video on string theory won't go into analytical continuation and Riemann function. That's not their point. Their point is to show something weird so that some kid somewhere will read up on it maybe and becomes interested in theoretical physics.

Do you really think that's how math's done on string theory courses? For fuck's sake, at my university the only string theory group is a part of mathematics department.

>>6289404
This video OP?

http://www.youtube.com/watch?v=w-I6XTVZXww

Well, this "bullshit math" is actually confirmed experimentally in the Casimir effect.

>>6290245
>>6290246
im prety sure OP means this
http://theoreticalminimum.com/courses/string-theory/2010/fall
5th epp.

I hope not, because that means OP is to retarded to even listen to words, since he repeatedly mentions stuff like
>this is the easiest way to show D = 26, but there are multiple other calculations that show it more rigorously
>the result 1+2+3+... = infinity -1/12 is usually half jokingly stated as 1+2+3+... = -1/12
>he shows how you can ignore infinities when its a additive constant using momentum as an excample

and then the best part of the OP:
> he also says that:
<div class="math"> \lim_{x\rightarrow 0}{\frac {1}{x}} =\infty </div>
>is true (it's not)

this part is just pathetic, nowhere in the video does he say this. he sais
<div class="math"> \lim_{x\rightarrow 0}{\frac {1}{x^2}} =\infty </div>
and if OP cant see why this is true while the first one is not, he is not a mathematician.

as for
>Not only is he having trouble finding a partial derivative and makes few mistakes along
its 9 o clock at night, after a day of teaching actual physics and doing actual physics, and the guys like 70, doing a string theory class for laymen. god forbid he strugles with some derivatives.

>>6290281
Thanks for calling him out.

OP, you are an ungrateful bitch who doesn't even listen what the prof is saying, fuck off

The thing about physicists and math is that they play rather loose with the rules and often make up unfounded methodologies as it suits them. Look at Feynman path integrals as an example.

All that matters to them is that the results make testable predictions which play out in the natural world, not that they are mathematically rigorous [though a rigorous mathematical backing generally helps one's case]. So, while 1/x as x goes to zero may not strictly equal infinity, using this as a rule is rather useful in physical situations.

>>6289781
>implying zeta function is given by that series everywhere in C

>>6289404
Is

<span class="math">\lim_{x\rightarrow 0}{\frac {1}{x}} =\infty[/spoiler]

Not true? (When approaching from +ve side anyway).

Also, don't worry OP, it's just as hilarious for us physicists watching you mathematicians attempting to do physics.

I see mathematicians taking physics classes all the time. They think it's an easy cop out for easy marks. They sit in a group laughing at how little maths we do. Then it comes to problem solving time and I see them sitting in a bunch attempting to blaze through the problem using their pure mathematics like a crutch.

One of the components is obviously 0, and by symmetry the answer is quite clearly 0, but the maths guys will try and blaze through some general triple integral without stopping to think about the situation while everyone else just writes "0" down on their paper.

>>6289404
>I'm dismayed at how carelessly and haphazardly physicists (ab)use math.

Your entire field of study is based on math. Of course you are going to be more rigorous than us when it comes to what is essentially just a tool for us.

It would be like me complaining how Engineers don't understand physics. They use tables and weird approximations without understanding any of the physics behind what they're doing. But who cares? It's not their job to know that. It's their job to build me a bridge as efficiently and safely as possible. Time spent on physics would detract from time spent on engineering.

I actually like mathematics, I'm more of a mathematical physicist than a physicist, I hate the lack of rigour and rote memorisation. But I'll never attain the level of pure maths that a mathematician has, I simply don't have time to do 2 degrees at once. I don't tend to bring it up around mathematicians because most are as elitist as you. "There's no point explaining because you won't get it"

Mathematicians are almost as bad as Computer Scientists at explaining things from their field to people of other disciplines. You're not quite as arrogant or jargony as they are but you're getting there.

>>6290246
>0:20 into the video
>camera shows his iMac computer
Stopped watching right there.

>>6290367
No, assuming /sci knows what analytic continuation is.

>>6290374
>I actually like mathematics, I'm more of a mathematical physicist than a physicist, I hate the lack of rigour and rote memorisation. But I'll never attain the level of pure maths that a mathematician has, I simply don't have time to do 2 degrees at once.

I did do 2 degrees, math and physics. From the moment I realized how beautiful math can be, I became unable to enjoy physics since they routinely strangle that beauty.

I would probably enjoy physics more if more physicists embraced the geometry of physics as opposed to feeding their addiction to partial differential equations.

>>6290374
physicists are the absolute worst at shitting up other sciences. they always look like idiots, too, when they do it.

>>6290374
Engineers are still TAUGHT the physics.
At least the macroscopic models.
But even my material science class tried to explain semi-conductors and energy levels.

Where do you think we make weird, unjustified approximations?

I'm think Nusselt number correlations (all of convection for me) Are experimental terms not good enough?

>>6289404
>really thinks that string theory is based on that
Lol

>>6290374
protip: engineers know the same physics as you do, but they can use it.

They're not looking to further find theories, they just know what the current ones are and how they're of use.

>>6290709
>protip: engineers know the same physics as you do

I studied it for a year, no they don't

>>6290719
> studied it for a year
lol

>>6290694
but it is.

>>6290709
>engineers know the same physics as you do
wat. engineer here (graduated) we did only very basic QM (basically no math) that can be applied to chemistry, Newtonian mechanics (no lag or ham), and very basic statistical mechanics compared to the physics guys. the only thing we did on the same level (maybe more) was thermo, electrodynamics and fluid,mass,heat dynamics. the only way an engineer will do the same physics as a physicist is if he focuses on it in postgrad.

>>6290734
No

>>6290762
well I'm an engineering grad student
QM doesn't matter for MechE's but I know EE's have to get to it at some point.

We briefly went over Lagrangian Mechanics in undergrad, but it's covered fully as a grad student. And then we get to study Kanes Mechanics (yay).

Got me on statistical, but we do Thermo just differently. Macroscopic models instead of microscopic


Totally covered more in heat, mass and fluids than physics majors do.

>>6290764
you know fuck-all about ST.

>>6290780
No
Do you?

>>6289667
Do you even Paul Dirac?

Physics student here. I read the title of your post planning to see an insecure math student mentally masturbating over one silly unimportant error his physicist friend made but then I read your comment. Holy shit who is this famous physicist!? You're right that not even the average community college physics teacher would be that bad.

Still I'm disappointed that you're stupid enough to think that String Theory is based on the assumption that the limit is -1/12. I haven't studied string theory at all, but I know that if it could be disproved in 0.002 seconds like that it would have been. It's like if you suddenly realize that all of modern chemistry is based on the assumption that 1+1=3, it doesn't mean that chemists are stupid, it means that you're stupid.

tl;dr You still a dumbass, OP. You shouldn't call yourself a mathematician if you're that stupid.

>tfw chem E major
>take math classes for minor
>no one can tell I'm actually a retard engineer who couldn't prove shit

hue hue

>>6290370
The limit as x->0 of 1/x does not exist. For a limit to exist, both the left hand limit and the right hand limit must exist (they do) and they must be equal (they don't) therefore the limit is undefined.

>>6292033
read the fucking thread dumbass
>>6289755

>>6292038
I got a math minor with my chemistry degree and I wouldn't consider myself mathematically rigorous. Mathematically literate, perhaps, but pleb tier to the math trolls on /sci for sure.

>zeta function values for sums

<span class="math"> \zeta(-2) = \sum_{n=1}^{\infty} n^2 = 0 [/spoiler]

If you sum up all the perfect squares you get NOTHING!

>lewillywonkaface.jpg

>>6292033
> Argument from authority fallacy ad nauseam... calls OP idiot.

k den

>>6289670
You're a special kind of stupid aren't you?

>>6292033
>physics student
So how's high school physics? Have they covered all the secrets of the universe with you yet!?

But solving a rubik's cube isn't that difficult at all, and I'd fathom that even a legally retarded could be able to solve it. It's all about memorizing certain movements and matching it to a pattern.

>>6292110
Argument from authority is a fallacy in proof. Otherwise it's no fallacy at all. I would trust Richard Feynman's ghost for information about qft before I would trust Amit Goswami. Why? Authority.

I am now thoroughly convinced you're not a mathematician because even the dumbest of mathematician knows what an argument from authority is.

>>6292136
Not yet but we're covering the math we'll need to understand before watching What the Bleep Do We Know all next week so we're getting there.

>>6289404
I'm a complete and utter retard but what is the whole 1+1 = 3 mean?

Is it referring to dimensions or something?

>>6292185
It's referring to dark matter and dark energy.

>>6289404
first year here, what is the limit as x approaches zero for 1/x?

don't know how to do TeX sorry

>>6292193
Does not exist since the limits from each side don't match.

I was sure that this serie was a troll by numberphile. Anyway if the sum of all integers = -12 then also the limit of the integral of x from 0 to infinity = -12?

>>6292133
>American
>pub

not even realistic

>>6292193
Three things are required for a limit to exist. There must be a left hand limit, a right hand limit, and they must be equal. The left hand limit is infinity. The right hand limit is -infinity. Thus the limit does not exist.

Here's a visualization of the limit not existing:
>>6289802

>>6292197
I'm not sure if <span class="math"> s\mapsto \int_{\RR} x^{-s} dx [/spoiler] can be analytically continued to -1, but if it can, there's no reason to assume that it coincides with the analytic continuation of <span class="math">s \mapsto \sum_n n^{-s} [/spoiler].

>>6290709
>protip: engineers know the same physics as you do
LOL. There might be a few subfields were your knowledge matches ours, but saying you understand physics as much as we do is just retarded.

You may know the "same formulas" as we, but at the end of the day, you're just blind appliers with very limited insight of the actual stuff you're dealing with. No real shame in that - the point of engineering isn't to understand nature.

>>6292242
Fuck off, we don't need that insight.

>>6292248
that's what I said, retard.

>>6292242
but I do understand that better than you do.

The whole point is to understand the physical phenomena first and the physical theories behind it.
Then you look for different models, suiting the applications you can think of.
Each model takes into account certain physical phenomena, and disregards others depending on how precise you need it to be.
Then you apply this model to predict a behavior or a result; or to find the dimensions and parameters of a system.

Engineering is just physics going further. Sure, I won't find any unification of the fundamental forces, but you can stay mad because I know as much as you do at the moment, I am more capable than you, and I forever will be.

>>6289755
Susskind's string theory lectures are basically pop-sci. Not that it's a bad thing, those lectures are great for beginners, but it's not even at the undergraduate level. Read Polchinski if you want to actually learn string theory, but of course this would be pretty difficult since your field of study is basically just glorified philosophy and is piss easy compared to physics (applied maths is cool though).

>>6292283
>but I do understand that better than you do.
Yeah, in the exact same way I thought I understood black holes after watching stargate. These are the typical words of someone talking about things way beyond him.

>>6289981
What do you want to prove with that?

>>6290400
You're so open minded.

>>6290709
>engineers know the same physics as you do
Okay buddy...

I've never heard of an engineer who uses quantum field theory on a day to day basis. Engineering is a good field, but I've noticed that too many engineers/engineering students are delusional about how much physics they actually understand. Electrical engineering requires you to understand the most physics, but the only electrical engineers who have even learned electrodynamics are those who have a PhD in the field.

>>6292305
let go, man. if you don't even allow them to masturbate each other at the idea they actually understand stuff, what pleasures will they have left?

>>6292083
know any good quick latech editors to check your shit?
i've been having problems posting shit on /sci/ because I'm too lazy to use miktex shit

>>6292283
>Engineering is just physics going further.
Engineering is just *using* physics; ftfy. Any retard can use a computer, but that doesn't mean he understands how it works.

>>6292283
>Engineering is just physics going further.
Engineering is just *using* physics. Ftfy. Any retard can use a computer but that doesn't mean he actually understands how it works. Is this analogy simple enough for you or are you going to tell me I don't understand how a computer works ?

s=1+2+4+6+8...
s=1+2(1+2+4...)
s=1+2s
s-2s=1
s=-1/2
1+2+4+6+8...=-1/2

>>6292300
top kek. Are you a freshman or something?
Get out of your basement. And go see what happens outside of /sci/, and see how real engineers are educated and trained.

>>6292305
Again, this is typical of a /sci/entist. You know physics is many other things other than QM and relativity, right?
Although applying those to real systems means understanding them.
I know about classical optics, ondulatory optics, electromagnetism, mechanics, fluid mechanics, electronics, cs, heat transfer, particle transfer, solids physics and QM ,thermodynamics, thermochemistry, chemistry and a bit of organic chemistry, and plenty more.

Open your eyes.

>>6292324
got the comparison.
Engineers need to understand how physics work though.
And to further my argument, I'll use your own comparison:
as a physicist, you know part of the phenomena are engaged in how a computer works.
as a engineer, you know all those, and you also know how to design one, or part of one.
as a retard, you only know how to use one, and you might add "not very efficiently".

>>6289404
>he's trying to prove that sum of all positive integers is -1/12
No.
He's demonstrating to babby how one obtains the factor -<span class="math">\frac{1}{12}[/spoiler] using the "smooth cutoff factor" (1.3.33) in the equation (1.3.34) but babby don't unnerstan, babby cry.

>>6292344
>I know about blahblah and plenty more
Maybe, but not nearly as deeply as me. You can whine all you want, friend, this is fact!

OP, what is the Ramanujan summation of the natural numbers?

>>6292324
>Engineering is just *using* physics.
So is everything that ~99% of physicists ever do. And most kids who get a physics degree are by no stretch of the imagination "physicists".

Where's that video of the engineer who won't calculate anything in front of that lawyer without his formula sheet?

>>6292573
http://youtube.com/watch?v=y2X52rS-ZLE

They're discovering the secrets of the working of our universe. What are you doing? Just playing with meaningless numbers.

>>6289839
And here I was thinking shitload was one word.

>>6289657
its defined in the set of natural numbers nitwit

>>6289404
the series:
1-1+1-1+1-1.... = 0.5 agreed?
let A be the series 1-2+3-4+5-6....
A + A = 1-2+3-4+5....
+ 1-2+3-4+5..... (attracting your attention to how it adds up: 1-2+1+3-2-4+3.... = -1+1-1+1-1+1 which is 0.5)
so 2A = 0.5 ; A =0.25
no time have to go watch this: https://www.youtube.com/watch?v=w-I6XTVZXww

>>6292741
you sound mathematically retarded. didn't you read a word of OP's post? proof from that video is nonsense.

>>6292331
elohel.
To find an error, work backwards, but start with the premise.
s=1+2+4+6+8+...
1+2s=1+(2+4+8+12+16+...)
=1+2+4+8+12+16
!=1+2+4+6+8+12+16

I think your six should not be there. Even then, you do:
>s-2s=1
>s=-1/2
When really, that would imply:
>s=-1

s=1+2+4+8+16+...
=1+2(1+2+4+8+16+...
=1+2s
-1=s

>>6292748
The reason why this "works" is because of the second to last step, we are assuming s is not infinity. If s=infinity, then s=1+2s is also true. In other words, working with an extended set, such as the extended reals, there are three solutions to the linear equation ;)

>>6292578
that's amazing - thanks

>>6292314
http://www.codecogs.com/latex/eqneditor.php

>>6292578
>square rut

>>6292331
last time i checked...
s-2s = 1
is not s = -1/2, cuz then s-2s = 1/2

:|

>>6292578
What the fuck is this?

>>6292962
Typical engineer when not sucking.

>>6293002
Nice try mate but engineers contribute alot more to the world than mathmatician

>>6293014
Not without their formula sheets!

>>6293034
>>6293034
you've memorized all the conversion factors and can pull them out of your ass in a stressful situation?

>>6293057
He gave him the factor.

Eh what? The limit as x tends to 0 of 1/x... IS infinity.

>>6293070
I couldn't watch the whole video, it was too cringe worthy.
Still, lawyers are scary.

Have you ever fucked up on an exam where you wouldn't have on the homework?

>>6293088
To be fair, the lawyer gives him the formula at one point. And he refuses it.

>>6293081
It isn't. It's a two sided limit hence it is undefined and doesn't exist. It's equivalent t division by zero. See the wikipedia link above.

>>6292039
Oh. For. Fuck's. Sake.
http://en.wikipedia.org/wiki/One-sided_limit

This thread is full of people who took a couple of courses in algebra and think that means they know what they're talking about.

Seriously.
Shut.
The.
Fuck.
Up.

>>6293097
And I've added 2 and 3 and gotten 6.

>>6293165
oh you stupid idiot.

https://en.wikipedia.org/wiki/Division_by_zero#Formal_operations

it's right there.

also, this is NOT A ONE-SIDED LIMIT YOU STUPID MORON.

Pic related.

>>6293165
>http://en.wikipedia.org/wiki/One-sided_limit
he said exactly what was in your wikipedia article.

are you illiterate?

>>6293176
>>6293181
missing a superscripted minus sign off something that is basically subscripted in the first place is hardly a crime worth crying over.

>>6293186
there's no subscripted -. and it doesn't even make sense to have it in the equation in question in the first place. do you even understand when issues like this arise? obviously not. go take some basic math classes, you pleb.

>>6293186
let me repeat myself:
he said exactly what was in your wikipedia article.

what was the point of your post?

>>6293176
too bad -inf = +inf in terms of complex analysis

>>6293197
no it doesn't...

residues become negative or positive due to the sign of the infinity

>>6293203
Not true

Only one infinity is considered in complex analysis

if you considered plus and minus infinity, you would have to also consider i(infinity), -i (infinity), in fact infinity in any angle, an infinite number of possible infinities, all of which are a distance of infinity from eachother

>>6290647
physicists are the most cancerous idiots in existence.

>>6293208
http://en.wikipedia.org/wiki/Residue_theorem
Residues are positive or negative, I think...
My notes didn't make it that far into the class.

Also you can just say it has infinite distance and has angle of departure whatever from control theory.
There's still a difference between + inf and - inf

They are in opposite directions.
You can also say + inf at departure angle a is the same as - inf at departure angle 180+a

>>6293221
It doesn't make sense for a residue to be infinite.

>>6293221
And again if you consider -inf and +inf then you kind of have to consider all infs, all infinity of them.

That's why only one infinity is considered

>>6293230
the residue isn't infinite.
it's formed from <span class="math">\frac{1}{z+1} [/spoiler] which is different than <span class="math"> -\frac{1}{z+1} [/spoiler].
I might be thinking of the direction of the contour looking further into it.

>>6293233
no you don't.
Certain complex functions come out to be real functions.
You can always define an infinity by an angle and a directional infinity.
It'd be easier to use the +inf, but that doesn't make -inf equal +inf

>>6293238
the residue is just the -1 coeffcient of a function expressed as a Laurent series

it doesn't make sense for this coefficient to be infinite

therefore this doesn't affect the fact that only one infinity is considered in C

>>6293242
I'm not talking about the residue. I'm talking about the singularity, which has direction

i fucking hate this board so much you don't understand

>>6293292
hurts your tiny brain, eh? why visit then? do you enjoy S&M or something?

>>6292305
>I've never heard of an engineer who uses quantum field theory on a day to day basis.
>Nuclear engineering doesn't exist

>>6292358
> knows qft
> can't into basic bending equations
> thinks bernoulli's equation works for anything
lol

>>6289879
>mfw there are people on /sci/ RIGHT NOW who didn't know this`

ITT: Engineers pretend to know more about physics than phycisists; /sci/ doesn't know how to do limits.

Uh... the answer isn't -1/12.
If that were true, how the fuck would simple integrals work?

>>6294160
From a math standpoint: we can define that equals sign however we want, and analytic continuation is a sensible way of doing so.

From a physics standpoint: we have observed the Casimir effect, so nature says that -1/12 isn't that crazy a value to assign to 1 + 2 + 3 + ....

Simple integrals, whatever they may be, work exactly the way you're used to.

>>6289758
You are the retard, it was defined in the set of natural numbers so no need to specify.

>>6294221
no, you are retarded.

>>6289404
ITT:fags still in undergrad maths like Linear Alg trying to disprove this guy.
Nope I checked his math out from the photo you posted. He checks out. Susskind just does renormalization on a limit and assumes the left sides limit.

>>6289404
nice troll thread

>>6294242
try to disprove OP or susskind?

>>6289410
How does one abuse something "Correctly"?

>>6289759
Ummm . . . If a limit is at infinity, is it a limit at all? Engineer here also.

>>6289802
Whenever I look at that, I see it on an infinite sphere with the origin at lat/long (0,0) and the lines crossing at the notional antipodes.

>>6294044
>mfw there are people who don't know as much about [the subject of my studies] as me

Yeah no shit

how do i divided by 0?

a real man / woman lives and dies.
the rest try (science math) some whacko shit. Then dies.

I know, I know, you want proof.
Catch the drift?

>>6295774
use the force.

OP is obviously brain damaged. I've seen about 4 different proofs of that, and two of them were done by mathematicians.

>>6297558
> I've seen about 4 different proofs of that, and two of them were done by mathematicians.

>argument from authority

And they're all wrong.

http://blog.rongarret.info/2014/01/no-sum-of-all-positive-integers-is-not.html

>Copenhagen interpretation
>1927
>"If nobody looked at the moon it wouldn't exist."
Physics jumps the shark

>String theory
>2014
>"The sum of all positive integers is -1/12."
Physics nukes the fridge

I dont understand. The series is divergent, yet apperently its a valid enough equation to work in string theory.

This has made me understand that I don't understand infinity. I don't understand limits. I don't understand when a series "equals" something.

I got an A in Calc 1-3 and Diff Eq but this single equation made me realize I don't understand a fucking thing anymore. I just don't

>>6297629
So is the 1-1+1-1...=1/2 false too?

I'm so broken

>>6297811

The last math class I took was junior year Algebra II, where I got a B+. None of this shit makes sense to me.

>>6297811
>It works in something that has zero experiments to support it!

>>6297813

It doesn't converge.

You try to converge a divergent series and you get whacky results.

Holy shit, who knew?

>>6292353
>babby cry
this

Strings of what?

>>6297944
The universe.

>>6297945
Yea, but what are they made of?

>>6297629
So you didn't even read the link that you posted? That blog agrees that you get that result via Ramanujan summation.
It's a non-rigorous result, but if physicists were obsessed over rigour like a bunch of autists they wouldn't even have special relativity. If it gives you the correct result like it does with QFT, then it's good enough.

>argument from authority
Arguments from authority are essential to pure mathematics. Since logic is subjective, a proof is not accepted unless it is accepted by the mathematical community. This is why physicists have experiments instead.

>>6298012
>logic is subjective
Are you retarded?

you are mentally diseased

http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

>>6298048
I read about half of it and realized I don't know what the fug is going on anymore. What is this saying?

>>6297968
Themselves or no one knows yet.

Strings are (according to the theory) what point particles really are (like electrons, photons, quarks ect.). What frequency the strings vibrate at decides what particle they are, because it decides how they react to other strings. The strings only seam like points to us because they are extra-dimensional (six extra). Dimensions like space and time are also strings, they are stretched out strings called branes,

>>6298012
>that you get that result via Ramanujan summation

that doesn't make it right either.

>>6298012
>Arguments from authority are essential to pure mathematics.

LOL

>Since logic is subjective
>Since logic is subjective
>Since logic is subjective

shut the fuck up.

>>6298745
>2+2 = 1
>NO IT ISNT!!!!
>calm down, im working in Z3.
>THAT DOESNT MAKE IT RIGHT!!!

so what i've learned from this thread is that 1+2+...n = -1/2 {R} is the perfect litmus for for folksy intuitionist rationalists who think math is something more real/logical/pure/whatever than just a numbers game

from being angry about divergent sums to being angry about subjectivism in like 3 posts

>>6298794
>folksy intuitionist rationalists who are unable to read
much hurr, little durr
>>6292353

>>6298811
i understand the proof i'm just saying it's funny how many people have such an impartial gut reaction to it

>>6298819
>i'm just saying
I'm just saying address the issue.

http://www.youtube.com/watch?v=E-d9mgo8FGk

PLEASE WATCHING THE SECOND PART OF THE VIDEO

EVERY FUCKING TIME THE FIRST PART IS MENTIONED, NO-ONE EVER TALKS ABOUT THE SECOND PART.

>>6298794
>what i've learned from this thread

you obviously haven't learned anything.

Are strings the physical manifestation of the non-trivial zeroes in the Riemann zeta function (frequencies)??