New proof!

>>8214255
lul. Might want to make sure that 1+2+3+...= -1/12

1+1+1 does not equal 2
i was expecting a good troll but u didnt even make it past the 3rd line

>>8214266
didn't make it passed the 1st line

>>8214266
1+1+1-1 = 2

Simply imagine that I grouped it like
((1+1+1)-1) and that does equal 2.

You are dumb. Don't you see the -1 that is directly after the 1+1+1?

>>8214264
Well, modern mathememecians say that the sum is equal to -1/12 so I was just testing that hypothesis.

Turns out they are full of shit.

File: fixed.png (166KB, 352x461px) Image search: [Google]

166KB, 352x461px

>>8214266
Revised version.

>>8214273
also you fucked up on line 4. While it is true that there are both infinitely many +1 and -1, there are ALWAYS at least 3 +1 for every -1, so it's > 0. That's an important aspect of infinity to understand.

>>8214264
Nah he's right. You can evaluate the sum as -1/12.
However OP check your third line, where you write 4 as (1+1+1).

>>8214288
>, there are ALWAYS at least 3 +1 for every -1

No that's dumb. There are countably infinitely many 1s and countably infinitely many -1s.


If you cut off the sum at any point all you need to do is look take some -1s from the sequence beyond that to make it all 1 + 1 - 1 + 1...

That is always true because there are infinitely many -1s, you just need to look further and you can always look further because it is infinity.

Accept that mathematicians fucked up and that we have to start from the beginning. That said, we should keep set theory as the foundation but we should just in case throw out all of the alternatives for set theory and anything that is supposedly before set theory like category theory which is just a meme.

>>8214291
>However OP check your third line, where you write 4 as (1+1+1).

Please check my revised version.

I am very proud of this proof by the way and none of you can prove it wrong.

>>8214291
LUL WAT.

https://www.wolframalpha.com/input/?i=infinite+sum+of+n+from+n%3D1

>>8214300
That is what I believe and what mathematicians used to believe but nowadays people claim that the sum converges to -1/12.

My proof shows that this result leads to a fundamental contradiction and therefore mathematics is wrong.

>>8214283
Even if you could just slide the -1s along like that, you wouldn't get
1 - 1 + 1 - 1 + 1 - 1 +...
you'd get
1 - 1 + (1+1+1) - 1 + (1+1+1+1) - 1 +...

>>8214299
Go to bed Professor Wiles, 4/10 for making me take the bait.

>>8214306
You are wrong.
Lets take a look at the finite part of your sequence

1 - 1 + (1+1+1) - 1 + (1+1+1+1) - 1 +

Tu turn that into 1 - 1 + 1 - 1... then you would have to find 5 more -1s because at the moment you have 8 1s and 3 -1s.

If you look further into the infinite sequence can you find 5 more 1s?

FUCK YES YOU CAN!

And this is true no matter at what point you cut off the sum. And why is this? Because you have both infinitely many 1s and infinitely many -1s.

This is pretty much pre-school arithmethic man.

>>8214309
I am not going to bed, just got back home from work. I have found a truly groundbreaking result and WE NEED TO ADDRESS THE PROBLEM OF INFINITY.

>>8214299
they are both countably infinite but one always has more member than the other.

borrowing -1 from beyond the 'cutoff' is adding 0 to the series, it changes nothing

>>8214320
No no real numbers can stay my man.

We just need to kick infinity the fuck out.

Changing the order of summation in divergent series is not allowed

>>8214322
>they are both countably infinite but one always has more member than the other.

Infinity is not larger than infinity.

To me it looks like no matter how long the sequence is, you can always keep finding -1s to pair them up with the 1s.

Also, what are you fucking with me for? It was these motherfuckers who started the grouping shit.

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

If grouping is now a valid arithmethic operation then I just thought I would take it to the next level. I mean, why not?

Why can they group and do shit like they want but I can't?

>>8214255
write up your paper and post it to arXiv. You're a misunderstood genius and I wish you good fortune.

>>8214332
I believe he posts under the pseudoname Victor

>>8214330
https://www.youtube.com/watch?v=w-I6XTVZXww

These bastards take an infinite sum and then shift it around so that they get what they want.

I am just doing the same.

Hold my beer guys. I got his!
1-1+1-1+1-1+1-1+...
1+(1-2)+1+(2-3)+1+(3-4)...
(1+1+1+1+1+...)+(1+2+3+4+5+...)+(-2-3-4-5-...)
(1+(1+1)+(1+1+1)+(1+1+1+1+1)+...)+(1+2+3+4+5+...)+(-2-3-4-5-...)
2(1+2+3+4+5+...)+(-2-3-4-5-...)
2(1+2+3+4+5+...)-(1+2+3+4+5+...)+1
(1+2+3+4+5+...)+1
-(1/12)+1
1-1+1-1+1-1+1-1+... = 11/12

>>8214331
yes infinity has many different sizes.

http://www.math.grinnell.edu/~miletijo/museum/infinite.html

>>8214340
>yes infinity has many different sizes.

A number a is bigger than b if and only if a - b > 0

infinity - infinity is an indetermined form.

The fact is that for every +1 there exists a -1 further along the series that will pair with it. Prove that statement wrong.

You can't because no matter how long you are in the series, it is always true that there exists another -1 deeper in the series.

>>8214299
Everyone is wrong. Clearly you take the rms. In this case, 1+1-1+1...=1.

You can always remedy bullshit with more bullshit.

>>8214335
LUL they are trolling dude and I hope you are too. n in the textbook is not the natural numbers lmfao

>>8214255
How much of a schizophrenic do you have to be pretend you are smart, do all this superficial stuff, and then die

>>8214343
There ISN'T always a -1 +1 pair for every +1 because there are MORE +1s. Every time you create a -1 you create 3 or more +1

Garbage in--garbage out. The garbage inbetween was optional.

>>8214345
I am not trolling because they are not trolling.

I am not saying my statement is a true statement. My statement is a false statement that happens because those bastards say that infinity = -1/12.

I am just proving them wrong.

>>8214352
Yes there is, just look deeper into the sequence.

Why? Because there is no point in the sequence where after that point the sequence is just +1+1+1+1+1+1+1+1+1...

That never happens, there is always another -1, even if it is really fucking far away.

>>8214283
The first line is incorrect and modern mathematicians do not say that -1/12 is the sum of 1+2+... That sum diverges. And then you fucked up even more by rearranging an infinite series incorrectly.

>>8214366
>modern mathematicians do not say that -1/12 is the sum of 1+2+...

Yes they do, and apparently physicists do too. Did you watch the video?

> That sum diverges.
Yes, this is what should happen but this theory has fallen out of favor and been replaced with the absolute meme.

>And then you fucked up even more by rearranging an infinite series incorrectly.

If the -1/12 memers can rearrange their sums then so can I.

Someone just read Abbott's analysis uh

>>8214373
No, I take analysis in 2 years.

I am freshman math major, just finished my first semester. All I have under my belt is calculus, geometry, set theory and (abstract) algebra which is what we learned this first semester.

Just that is enough to fucking break down math.

>>8214358
lmfao dude, for example he's trolling when he gives s1 = 1/2. He can hardly contain his laughter. The series diverges - it 'equals' nothing

>>8214376
That is what I say!

But then the memers just keep going and I am proving them wrong.

If you ask me they sound pretty serious about the shit they are talking about.

>>8214372
> Cesaro sums
> "equal"

>>8214382
I've heard of that but the memers did not once mention them in their video.

By the looks of it they are supposedly just using normal arithmethic to get that result.

AND THAT IS WRONG. So I prove it wrong.

>>8214380
here's a link to the pdf of the physics textbook they reference at the beginning.

Go to page 23. n is not the nautral numbers, it's a renormalize lorentz invariant lmfao dude they are trolling relax

>>8214394
didn't give the link lol here

http://stringworld.ru/files/Polchinski_J._String_theory._Vol._1._An_introduction_to_the_bosonic_string.pdf

>>8214386
Well if a problem has an answer that can be found by doing 1 + 2 + 3 + 4 +5 ... at some point it may secretly be asking you to evaluate the Riemann-Zeta function for s=-1, which is -1/12 via analytic continuation.

Not the same as really doing the sum but if you replace the infinite sum with -1/12 the value may be the right answer for the problem, which you might be able to verify by solving the problem using a different method that entirely avoids the infinite sum but gives the same answer.

>>8214372
>Yes they do, and apparently physicists do too. Did you watch the video?
No they don't. Did you try to learning about what you're talking about instead of watching a youtube video?

>Yes, this is what should happen but this theory has fallen out of favor and been replaced with the absolute meme.
No it hasn't.

>>8214394
>>8214396
No fucking way.

Then why the fuck did they make that video? Holy fuck.

The guy looks so serious too. Do you know that numberphile meme with the copypasta saying something about the number 5 and a guy sweating looking really excited.

The bald guy talking about -1/12 looks just like that. Like he is seeing the face good and god is smiling at him tellimg him "Yeah, you did big boy. You proved the sum big boy."

>>8214399
Well, the faggots mention Riemann but they do not use the zeta function. They just sum divergent serious like it ain't a big deal.

>No they don't. Did you try to learning about what you're talking about instead of watching a youtube video?

I don't know when we will be introduced to such sums.

>>8214255
You can't watch just one video and then make shit up. You have to watch this video as well: https://www.youtube.com/watch?v=PCu_BNNI5x4

>>8214404
No they don't use the Zeta function, using Ramanujan's way kinda lucks out at the right answer but is misleading in what it is actually saying

>>8214404
>Area Man Learns That YouTube Videos Not Actually Authoritative Source For Mathematical Knowledge

No actual mathematician, anywhere, believes that summing all the natural numbers literally totals to -1/12. However, if you are in the business of making pop science videos and are just skimming Wikipedia for stuff that sounds crazy, you could certainly think "WOW! 1 + 2 + 3 + 4 ... actually equals -1/12! Isn't that crazy and unintuitive? Oh man, this is going to blow my subscriber's minds."

The methods used in the Numberphile video are also completely illegitimate; you simply can't just shuffle around divergent series like that, it's undefined. You can easily prove 1 = 2 with such methods.

The -1/12 figure actually comes from analytic continuation of the Reimann Zeta function. IIRC, I think it also pops up in Ramanujan summation, which is a way of assigning values to divergent series (NOT their actual total!)

The Numberphile video received wide criticism from actual mathematicians and was a major meme for a while.

>>8214330
This is the closest to a real argument against the OP being correct provided in this thread and even then it doesn't actually provide a proof or a reference to an established axiom of why this is the case.

Overall the quality of responses in this thread shows that Most of you are much less mathematically knowledgable and skilled than the OP

>>8214430
Alternate explanation: We had this same goddamn thread nearly a thousand times in 2014 and 2015, and nobody is going to bother putting in any more effort to explain why no, the sum of all natural numbers is not negative one-twelfth.

Also, anyone who believes it doesn't know enough math to be worth the effort trying to explain; you have to believe that math is some kind of mystical, esoteric thing where anything is possible in order to believe that adding an infinite sequence of positive numbers really produces a negative one due to some ineffable glitch in the fabric of arithmetic.

>>8214430
>you can't change the order of summation in a divergent series therefore you're wrong

if the series was given to be divergent then you wouldn't have to prove it doesn't converge to -1/12......

get out of here with your retarded high horse

>>8214305
No one claims it converges or sums up in the conventional sense.

Numberphile is just supposed to be an introduction to math; it's a meme because people take popular media seriously.

>sum of positive numbers is negative
has science gone too far

>>8214305
It sums but it does not fucking converge. That is the crucial fucking flaw in your """"proof""""

>>8214502
Also, 1+2+.... is a divergent series so you are not allowed to rearrange terms like you did.

the shifting around is shady as fuck
also how does the sum of whole numbers turn out to be a fraction. how does the sum of fractions go on to infinity?

>>8214534
>how does the sum of whole numbers turn out to be a fraction
how's high schul treating ya bro

>>8214255
Mathloger made a video about that a while ago. If you organize the series in that way you're gonna run into some weird shit. https://www.youtube.com/watch?v=-EtHF5ND3_s

>>8214543
How are meme videos treating since you obviously don't understand what the -1/12 means?

>>8214507
................................................
if it's GIVEN TO BE DIVERGENT you don't have to PROVE IT DOESN'T CONVERGE. Stop memeing about term rearranging

>>8214343
This is a good troll.

>-1/12=1+2+3+...
shiggy riggy diggy

>>8214563
It's conditionally convergent which is important to the rearrangement. Term rearrangement isn't a fucking meme.

I am facepalming so hard rn. Please take an introductory-level analysis course and then come back when you understand how series work.

>>8214255
Day/Month/Year
Thanks for saving my time and letting me know youre a retard.

>>8214726
>ascending order
>retard
Stupid burgers, go back and support your horrible election candidates.

>>8214719
Was that basically a "git good m8"?

>>8214255
https://www.math.washington.edu/~morrow/335_14/history%20of%20rearrangements.pdf

>>8214746
Yeah. Come at me, bro.

My people!

I know you are sad that I proved that all the mathematics since the 18th century is flawed but WORRY NOT.

I start the process of rebuilding in my other thread >>8214602 with an amazing identity that rivals even euler's identity.

Please PhDs, take my result and rebuild mathematics.

YOU CAN DO IT!
WE CAN DO IT!

We just lost 200 years but I am sure we can rebuild it back in about 2 years with my power.

>>8214900
We can start by abandoning the Reals.

the first line is wrong

>>8214694

> 1 + 2 + ... is divergent
> it's conditionally convergent

please do us a favor and rid this conversation of one more convinced retard

>>8214255
(-1/12) = 1+2+3+4+5+......
no its not u fucking kek
lim(1+2+3+....+n) =-1/12
as n->inf

>>8215521
>lim(1+2+3+....+n) =-1/12
>as n->inf

what the fuck, why?

>>8215521
That is the same thing. In the limit of a sum you are simply adding infinitely many terms.

That lim to infinity is literally just the sum so I am still right and all of mathematics is therefore wrong.