How much of a brainlet do you have to be to believe this nonsense?

>wat is rigor

Stop being such an autist. That video is for show. For people who don't know analysis.

Everything in that video is rigorous if you construct a method of summation such that 1-1+1-1... converges to 0.5, and a such that whatever other sum they play with there converges.

And surprise surprise, such methods do exist you mouth breather. It is only that you can't fit hundreds of years of analysis into a youtube video.

but if we say that 1-1+1-1+1-1+...=x
then x=1-x
2x=1 x=1/2

Most people couldn't even give a definition of an infinite sum in analysis. The question is moot.

It's a meme for SCIENCE IS COOL faggots who don't know what the zeta function is. They apply the series definition when it doesn't exist and the function is defined by analytic continuation. It's just wrong

>manipulating a non convergent series like that

Can someone explain the -1/12 meme to a non mathematician?

i haven't even got to calculus and know, from a base rational level that infinitely adding numbers doesn't get you -1/12, it just gets you an infinitely high number.

it's simple really. I don't know why you retards don't get it

The real question is how much of a brainlet do you have to be to actually go out of your way baiting people into disbelieving several great mathematicians

I think it was originally discovered by Ramanujan (a very famous indian mathematician who obsessively did math in isolation in his shit hut despite only a shitty indian education)
Several other mathematicians agree with him. Look it up on youtube under numberphile

Except it fails at its premise because it does not converge to 0.5.

X does not equal one finite number and thus doesn't even satisfy the definition of a function, let alone a series

[eqn]1-1+1-1.... = (1+1+1...)-(1+1+1...) = -\frac{1}{2} - (-\frac{1}{2}) = 1[/eqn]

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.

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

Brainlet here, If this infinite sum stuff was revealed as nonsense how much of what we thought would change

Does anybody here get tired of base 10 shit?
I'm no mathematician by any means, but I do think that different representations may offer some insight into different problem :p

-1/12 is so fucking stupid

it's literally the closest real mathematics can get to those retarded old ass "hold magnet in front of car for free thrust" troll images.

Serious question:
Is saying that than sum is equal to Aleph null wrong? Or are the aleph numbers just used in set theory?

youtube.com/watch?v=sD0NjbwqlYw

>all those brainlets that can't comprehend the value of an unrigorous but intuitive explanation

I challenge you to write a program that appears to attempt to calculate the sum of the natural numbers...
but by clever abuse of floats/pointers/whatever returns -1/12.

If you should succeed, CS will be elevated to the much-sought position of Current Sci Meme Degree.

Surely it's just a coincidence that extrapolating the curve to x=0 yields a y-intercept of -1/12, and this whole meme definitely isn't a result of brainlet compsci "approximation"

This is the same human error bullshit as the double slit experiment and every normie who thinks they understand Schrodinger's cat and paraphrases the Heisenberg uncertainty principle

You can interpret each term of the series as a cardinal number and then the sum would be alef null

I doubt any good such curve is known. What do you mean?

go to the wikipedia page and look at the line of best fit, goes straight back to -1/12
Also, it'll tell you that this whole meme is a result of Ramanujan summation, which was never intended to actually represent divergent sums
It's a human estimation tool that's getting misrepresented for controversy, same way Heisenberg uncertainty has nothing to do with what particles are actually doing and everything to do with our inability to observe them
It's just humans being dumb again, I would bet a large amount of money compsci is partially to blame

omg lol

What's the formula for the curve?

I dunno, go read it
It takes less than 30 seconds of research to find the math behind why this whole -1/12th meme is bullshit, literally google "sum of natural numbers"

Yeah, I searched. A Terrence Tao blog is related, but I see no formula for the interpolation and Wikipedia only shows the picture

That's because the formula is "take this infinite sum, and extrapolate backwards"
It isn't a y=x style function

>extrapolate
yea but how do you extrapolate.
There are many ways to fit a curve to the sum.

"The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯. The parabola is their smoothed asymptote; its y-intercept is −1/12"
My bad, so it wasn't backwards extrapolation, it was the EBA
But we both should have just read that

I don't understand, why is it a meme?
I mean it is counter-intuitive but the proof in the video seems solid. Why is it wrong?

Nobody (apart from physicists, maybe) is saying its a convergent series or that it converges to -1/12. What they are saying is there is a way to extend the concept of an infinite sum to non-convergent series and if you do that the number you get is -1/12.

It isn't the infinite sum of the series, it's a methodology to assign a unique number to a series. The fact that when you apply it to a convergent series you happen to get the inifinite sum is meaningless.

>extrapolating the curve to x=0 yields a y-intercept of -1/12
It doesn't.

can you provide any theorem or proof or rigorously stated axiom that says you cannot manipulate an infinite series like that?

then fuck off?

is the formula not y=0.5x^2 + 0.5x ? that literally gives the exact values for the sum, not some bullshit decimals.

Yes. The fit isn't perfect. It should be pretty obvious that the values for [math]B_1[/math] and [math]B_2[/math] are 0.5 and not 0.500000000000003. Same for the intercerpt. It's 0, not -0.0000000000007.

From the image linked in this post it looks like the value at -0.5 might be -1/12.

>From the image linked in this post it looks like the value at -0.5 might be -1/12.
Oh wait, no. It's a parabola. It's never going to be less than 0 with those parameters.

>Since 1-1+1-... oscillates between 0 and 1, let's say it's a 1/2
REALLY MAKES YOU THINK

LMAO, Veeky ForumsKEKS STILL THINK MATHEMATICS IS INFALLIBLE AND NOT JUST ANOTHER HUMAN TOOL LIKE A HAMMER OR A NAIL

AHAHHAHAHAHAHAHHAHA