>no /sci/ humor/ylyl thread

>>8705077
Ok, mathfags, excuse my brainlet question, but how the fuck can 1+2+3+4.... not equal 1+1+1+1....? Any number is a sum of some number of 1s, so it's just the same thing rearranged a bit, no?

How is the -1/12 thing derived?

>>8705843
https://www.youtube.com/watch?v=w-I6XTVZXww

This is simplified but they link to a more hardened proof. Note that it doesn't actually "equal" -1/12 because it doesn't converge, but it is intimately related to -1/12.

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>>8705077

>>8705843

The Riemann zeta function is defined for real part of s bigger than one: 1 + 1/2^s + 1/3^s + ...

You can show it extends to a function for all complex s, although the formula 1 + 1/2^s + 1/3^s + ... doesn't give you the function anymore when s is arbitrary. It happens that when you plug in s = -1, you get -1/12. That's all there is to it.

>>8705077

Even though the Reimann Zeta Function comes out to -1/12 would it still apply in the real world?

Wouldn't they both kill the same amount of people in the real world?

>>8705848
So it's all based on stating that 1-1+1-1... can be evaluated as 1/2? What you've done is made the operation no longer strictly equivalent to addition, don't you think?

>>8705865
Infinite sums don't represent anything that can come out in the real world by definition, since there is not an infinite number of anything in the real world. It appears to be mathematicians playing with definitions more than anything else.

>>8705867
Right.

>>8705077
>explaining the joke
This is fucking stupid. You shouldn't spell out to newfags what the joke is. The original version with just the two tracks and no text is the goat

>>8705893
Ok, I guess now I can sleep at night at least.

>>8705077
Did you fucking add text to that joke?
You may as well put the ifunny watermark faggot

>>8705913
The real joke in OP's pic is that the person who made it is such a newfag that they know that ζ(-1) = -1/12 but don't know ζ(0) = -1/2

>>8706018
I actually got it from here and saved it to use as bait

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my favorite hit single from /sci/

>>8706106
Cauchy was a mistake

>>8706114
He really was.

>Daily reminder that Cauchy used the so called Cauchy-criterion before even properly proving it.

I call it the brainlet-criterion now.

>>8705077
i dont get it

>>8706122
did cauchy fucked you are wife?

>>8706154
Cauchy fucked with the only thing I care about, rigor.

>The Cauchy Criterion is named after the French mathematician Augustin
Louis Cauchy. Cauchy is a major figure in the history of many branches of
mathematics—number theory and the theory of finite groups, to name a few—
but he is most widely recognized for his enormous contributions in analysis,
especially complex analysis. He is deservedly credited with inventing the epsilon-
based definition of limits we use today, although it is probably better to view
him as a pioneer of analysis in the sense that his work did not attain the level
of refinement that modern mathematicians have come to expect. The Cauchy
Criterion, for instance, was devised and used by Cauchy to study infinite series,
but he never actually proved it in both directions.

He was a brainlet.

>>8706162
"requiring proof" is a concept that grows and evolves
many things were assumed to be true by great mathematicians of old times and they wouldn't have thought that they actually required a proof

rigor is cool, but it's a modern addition and in no way the only valid mathematics

>>8706189
>many things were assumed to be true by great mathematicians of old times and they wouldn't have thought that they actually required a proof

And you know what we call those mathematicians? Brainlets. We shoud credit all achievements and theorems to the people that formalized them, not those who first "showed" those theorems.

In case you don't know, it was Weierstrass who took Cauchy's Cours d'Shit and turned it into formal mathematics. I call the cauchy criterion the Weierstrass criterion for cauchy sequences now.

If you don't do the same then you are probably a brainlet as him.

>rigor is cool, but it's a modern addition and in no way the only valid mathematics

Did you really just fucking say this? That we can have mathematics without rigor? Fuck off, you retarded freshman. Holy shit. I am sorry you failed your intro to proofs class but there is no way around rigor, pal.

Daily reminder that shit like this happens:
https://en.wikipedia.org/wiki/Italian_school_of_algebraic_geometry

>>8705077
But 1+1+1+... =-1, 2 with reimann's zeta function tho

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>>8706162
>>8706197
Do you refuse your dinner, sir

>>8706203
>Shall I refuse my dinner because I do not fully understand the process of digestion?

Nice meme quote you got out I fucking love cancer.

>The quote above is in reference to Heaviside using mathematical operators that were not yet clearly defined by the mathematics community.

Topkek, what a brainlet. I would answer your question but I don't really have to entertain the questions of a brainlet. Confront me with a mathematician who wasn't retarded.

>>8706106
fucking kek

>>8706211
I don't even debate the necessity of rigor. I simply point out the terrible truth that definitions always came later. There would always have been a Cauchy, and always have been a Weierstrass, but without Cauchy there would be no Weierstrass.

>what a brainlet.
Heaviside didn't need to be pampered by an entire mathematics department. Mathematicians caught up to him, not the other way around.

I'll ask you again: do you refuse your dinner, sir

>>8706236
>without Cauchy there would be no Weierstrass.

I disagree. I think that with enough study of sequences one would eventually realize that converging sequences behave "Cauchy". Weierstrass would have realized it too and he would have rigorously established them.

After all, Weierstrass came with a proof of the Cauchy criterion because Cauchy did not even understand his own definition well enough to prove his theorem.

I mean, to this day I do not understand what happened to Cauchy. The proof just involves applying the triangle inequality. Was the triangle inequality too hard for Cauchy? I mean, why? Why would he not prove it.

Nowadays, proving the cauchy criterion is a standard problem in analysis books for newcomers. (I know because I learned through Abbot's Understanding Analysis). If a bunch of freshman cucks like me could prove the cauchy criterion then why couldn't Cauchy?

This really, unironically, makes me think.

>>8706251
Because hindsight is a hell of a drug, also he probably had more important shit to do than prove some shit that already worked, like having sex with women.

>>8706251
>>8706211
>>8706197
You've been misled by the hard formalism of modern mathematics. It's not the goal, it's not the purpose, it's just a tool. Mathematics is done with silly pictures and fuzzy notions, by idea first and proof later. Dry, finished topics where you merely deduce obvious things from amazingly convenient definitions like a robot are not how mathematics is done.

I would kill 0.999... people because that is less than 1

>>8705077
If you explain the joke it's not fucking funny anymore. Half the humor is in awarding yourself for being clever for figuring it out. That's why enigmatic jokes are funnier.

Literally delete this.

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done for now. i better get some (You)'s

>>8705077
I mostly just browse /sci/ keeping to myself because Im only in high school and most of this is way over my head but can someone explain how hell that ends up being -1/12

>>8706605
rude!

>>8706645
use

>>8706669
you're too young, but look up riemann zeta function
[math]
\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} \\
[/math]
evaluated at negative one
[math]
\zeta(-1) = \sum_{n=1}^{\infty}\ \frac{1}{n^{-1}} =\sum_{n=1}^{\infty}\ n = 1+2+3+\ ... \\
[/math]
but by analytic continuation
[math]
\zeta(-1) = -\frac{1}{12}
[/math]

Anyone have that screencap of the joke where someone tries to steal 1/12 of a dollar from you by keep giving you money?

>>8706669
You first show that there is a unique function [math]\zeta(s)[/math] defined on the complex plane (save a countable set of points) that agrees with the expression [math]\sum_{n\ge 1}n^{-s}[/math] whenever Re(s) > 1. Then you show that this complex function necessarily satisfies the following relationship with itself [eqn]\zeta(s) = 2^s \pi^{s-1} \sin(\pi s/2) \, \Gamma(1-s) \, \zeta(1-s)[/eqn]
It follows that [math]\zeta(-1) = -1/12[/math]. After that you go back and pretend [math]\sum_{n\ge 1}n^{-s}[/math] also makes sense for s = -1 and make erroneous claims.

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>>8706822

>>8706848
Thank you, appreciate it.

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>>8705077

>>8705843
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

>>8706197
Do you even math, bro ? Rigor is needed for paper publication and/or when the results are deeply complex and/or subject to a lot of particular cases.

Any result where the counterexample(s) must be built ex-nihilo using whatever technique are informative and interesting, but any decent mathbro will call it pathological. Being pyschorigid only makes YOUR penis harder, smartlet.

>>8706211
you sound like a sophomore in undergrad just finishing up your first class on rings

fuck off you Berty Russ wannabe faggot

>>8706147
How would one multiply in binary without doing base conversion?

>>8706605
>1+1+x = 3
>x = 1
LOL FUCKING PHYSICISTS AMIRITE

>>8707565
1011x0110=10110+101100. For each ones digit in the right number you shift that many times and add.

>has shitty commentary on it

>>8706044
Based on that, is the decision based on algebraic or absolute value? Do you save more or less part of a negative person?

>>87058491
haha dude dank meeeme!

>>8708250
I didn't know you could save any one part of a human to begin with.

I mean, wouldn't that be stealing? Because it's the person's property.

>>8706645
for mu

>>8706729

Am I missing something or does this thing diverge and obviously has no finite answer

>>87058491
underageb&

>>8705833
Does this have something to do with a sphere

>>8709272
What you're missing is outlined here
>>8706846

>>8706162
It's from Abbot's book, am I right?

>>8706616
To his defense: If he's from Europe, chances are high that he's used to 1 in the shape of ´| and not just |
So his brain could only see two lines and not digits. It's damn hard to solve such a "riddle"

>>8709330
Psi function is usually orbitals of atoms.

>>8705089
indeed

>>8706106
I remember that thread, shit was unreal

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>>8705077

>>8710859
Pretty good

>>8707565
mul arg1 arg2

Lets multiply these two:
11 * 100

We have 100 + 100 + 100.

100 + 100 is 1000
1000 + 100 is 1100.

That's 1100.

>>8710978
Yea, thats O(n) tho (n being arg1 in your example). Which is retardedly slow if you want to multiply 5000000 with 10000000 for example.
What you want to do is this: >>8708105
Because this is in O(log(n)) (or however you want to call your parameters).

To pick up your example you would do this:
100 * 11 = 100 * 10 + 100 * 1 = 1000 + 100 = 1100

>>8706524
L O S T
>Thank you enlightened one

>>8706604
fucking gold

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I fucking love these.

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>>8706616
>mfw I thought it was some double line symbol
>mfw I'm an engineer

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>>8709335

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>>8711516

does anyone have the wildberger picture
you know the one

>>8711569
which one? The count picture, the "This circle and line don't intersect" picture? Wasn't there another Wildburger picture?

>>8711573
The "wildberger is thirsty" picture

>>8706142
Are those definitions of 1?

>>8706450
This. Modern proofs of Gödel's incompleteness theorems are extremely straightforward: make Gödel numbering, define loads of functions, prove diagonal lemma, plug a sentence you need in it and that's basically it. You might wonder what's the big deal with it. I know I did.

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>>8706616
>mfw I did not recognize any of those symbols
>mfw I'm a pure mathematician who have not used number since undergraduate

>>8711564
Oh, got it.

>>8706604
That is pretty freaking brilliant.

>>8705833
kek

>>8706729
>evaluated at negative one
It doesn't help that you and everyone else keeps pretending or at least implying that analytic continuation somehow means that the function is still magically defined as that series. This is what confuses people.

>>8706645
How is that funny?

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>>8711587
This one?

>>8711564
jesus christ

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>>8710867
lost

>>8711487
What am I missing here?

>>8706598
lel

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>>8705849
>Terry Tao
>YELLOWED.COM

>>8705848
what the hell is wrong with those people's faces and facial movements?

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>tfw to inteligent for math

>>8706995
What's the formula for that curve?

>>8705849
The fact that "dude infinity lmao" isn't written in caps always triggers me.

>>8711506
I see a doggo

Why do I always seem to find myself at a train switch with two infinite lines of victims?

>>8710867
lost hard

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>>8710331
>>8705833

>mfw remembering back to quantum chemistry in college

>all these brainlets implying that the sum of the series is equal to -1/12 even though equality can only be proved through convergence

>>8706604
This is my favorite picture the internet has produced.

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>>8709335
Jesus fucking christ there's no way people are this bad at CS:

int a = a.getLabel()
GUI.cards[a].setDone(true);

>>8709335
this is like, if someone wrote a program that wrote programs.

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How my professor likely spends HER evening

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>>8705849
>MATH PHD DROPS ACID

>>8711473
Holy shit I hope to god this is meant to be ironic

>>8714493
Not that guy but I'm pretty sure it's not.

>>8714205
>Formula
Kek

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>>8714459
You got it

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>>8714358
Jesus fucking christ there's no way people are this bad at CS:

int a = a.getLabel() - 1;
GUI.cards[a].setDone(true);

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Okay Sci, what if we take a happy little image recognition neural net, and plug it into the output of a scanning self referential bitmap formula, as well as one more neural net that could compare image output to current real phonographs of transpiring events, so that the engine will with a specific reference for time, be able to search images it believes are true to reality, from the bitmaps potential configurations, enabling the user to see in time to the best ability of the neural nets.
essentially its a high tech chronovisor idea, what do you think?

>>8714549
dammit i thought i was starting a new thread for fucks sake, that's annoying as fuck.