>changing the meaning of equals when you feel like it isn't postmodern, critical theoretic, sjw nonsense.
The sum of all positive integers doesn't equal a real number you fucking brainlet.
the only way it would is if it converged, which it does not.
now fuck off.
If you want to actually do something productive an rigorous then come up with another word or symbol for the relation you want to express between -1/12 and the sum of all natural numbers. You can call it "magic equals" if you want. you can use the symbol ~> if you want.
But stop being a subversive little shitter spreading fallacies and disinformation claiming that 1 + 2 + 3 + ... = -1/12 because that is a patent fucking falsehood.
I guess you can't expect much out of someone who makes a thread just to reply to a dead post.
Elijah Perez
>no argument
kill yourself, brainlet
John Moore
>I don't know complex analysis but here's my opinion on math ok then
Nicholas Rogers
this has nothing to do with the notion of equals you fucking brainlet. of course its true that 1 + 2 + 3 + ... does not equal -1/12 in a naive formulation like other brainlets like to spew, but using complex analysis it isn't hard to make such a rigorous formulation. come back when you graduate highschool
Jacob Jenkins
OP you seem really passionate about this whole -1/12 thing. Watch this video: youtube.com/watch?v=w-I6XTVZXww. I think you'll like it.
Ethan Perry
I fucking hate this meme.
Isaiah Long
Ok user, give me the "correct" definition of equals then.
Aiden Moore
i disagree because you are racist
Jacob Long
their worst video by far Don't explain anything useful, just muddy the water even more They should all be bitchslapped
But my dude, the "=" sign used in the typical convergence of infinite series is not even the same "=" used in, for example, 1+1=2.
The "=" operator has been overloaded countless of times. Why is that in this particular instance you complain?
Elijah Johnson
This. They don't even explain how it is equal to it and instead make it seen like that if you were to add up all the positive integers you would get it.
Angel Scott
He's right though. At the very least the summation operator should to be marked to deal with the various extrapolations of it, instead of just being all like "dude, obviously it should just be the analytic continuation, who cares" and acting like it shouldn't matter how that came about.
Jaxon Jackson
Alright if you're going to be such a fucking autist that you can't handle pop-math oversimplifying the subtleties of the subject for those that don't read math papers for fun, just change the equation into [math]{\sum\limits_{n\geq 1}}^{[\mathcal{R}]} n = -\frac{1}{12}[/math] and be done with it if you want rigour and not "muh subversive sjw math", read an actual paper on the subject: algo.inria.fr/seminars/sem01-02/delabaere2.pdf
Jace Rivera
The = sign of convergent series is actually the exact same relationship as in [math]1+1=2[/math], because the limit of a convergent series has a single defined, usually real value. The sum of a convergent series is just a real number, so its equality is exactly the same as in [math]\pi + \pi = 2\pi[/math]. Equality isn't ever really overloaded, except that it can act on different sets; it always has the same property of [math]x=y\Longrightarrow P(x)\leftrightarrow P(y)[/math] for all P. OPs problem is that he's too autistic about this when reading informal forum posts to accept that non-standard summation is used.
Jeremiah Smith
you mark things when you're uncomfortable with them to use them as they're used when you're a big boy
if idiots take it to mean usual equality of numbers, that's too bad for them for being retarded
Adam Nguyen
>so late to come up with a comeback he needed to make new thread hahahahahahahhahahhahahaa
Evan Nguyen
What I find dishonest is when people even write the sum of positive integers. For one, that's not the fucking prescription for the analytic continuation of zeta for Re(z) < 1. People literally lie when they write this shit or claim something that it "equals in a different sense". Fuck no it doesn't, the continuation equals -1/12 at z = -1
Sebastian Rivera
Typical equality is [math] A = B \iff ( x \in A \iff x \in B ) [/math].
Equality in convergent sequences implies that for every epsilon there exists an n such for that for all N bigger than n, the distance between the limit and the Nth term is smaller than epsilon.
If you tell me "Please forgive me. You have such a big cock and I have such a small tiny cock. That is why I need to contradict people on the internet even when I'm completely wrong." then I'll forgive you.
John Rodriguez
Please forgive me. You have such a big cock and I have such a small tiny cock. That is why I need to contradict people on the internet even when I'm completely wrong.
Noah Ward
>>changing the meaning of equals when you feel like it isn't postmodern, critical theoretic, sjw nonsense. This has not happened except in pop-sci explanations for brainlets who do not understand math.
>The sum of all positive integers doesn't equal a real number you fucking brainlet. Yes and nobody claimed otherwise except pop sci retards.
You are critiquing something without understanding it, the prime fallacy of a brainlet.
Adrian Price
I forgive you.
Caleb Nelson
Pop math brainlet here. The proof they use in the numberphile vid is trash, since's it's moving infinitely many terms of a not-necessarily-convergent series. But isn't there a rigorous proof actually using real math with the Riemann Zeta? If there is, then what's the problem with the result? I don't have a problem with counterintuitive mathematics.
Noah Bell
they literally link the Tao article in the pinned commentary you humongous faggot