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/sci/ - Science & Math

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3558551 No.3558551 [Reply] [Original]

You see this dude right here? Smartest man to ever walk the earth. Srinivasa Fucking Ramanujan. The man. And you know what he said? He said that if you add up all the natural numbers, you don't get some faggy "divergent series." No sir. You get -1/12. That's right, I said -1/12. What now aspies?

>> No.3558560

the fuck

>> No.3558561

>>3558551
>proof needed

>> No.3558566

>>3558551
Wait, which ones are the natural numbers?

>> No.3558568

>>3558566
whole numbers <-1

>> No.3558569

>>3558568
meant to say >-1

>> No.3558574

T = 1-1+1-1+...
-T = -1 +1 -1+1-1+1... = T-1
2T=1
=> 1-1+1-1+1... = 1/2

>> No.3558592

>>3558561
He never even bothered to prove it. He just wrote it down in a notebook and moved on, I guess because he found it self-evident. He was that good.

>> No.3558612

>>3558592
are you gonna provide any source or is this just a lazy troll thread?

>> No.3558627
File: 425 KB, 1920x1200, 1294671311049.jpg [View same] [iqdb] [saucenao] [google]
3558627

>sum of all natural numbers
>-1/12

I'm going to have to disagree.

>> No.3558630

>>3558612
you dont really need proof that adding all the natural numbers is a divergent series do you?

>> No.3558668
File: 20 KB, 275x338, rollbread.jpg [View same] [iqdb] [saucenao] [google]
3558668

>> No.3558685

>>3558612
Why certainly.
http://www.physicsforums.com/showthread.php?t=149279

>> No.3558708

ramanujan summation is a way to assign a finite number to divergent sums in a meaningful way which sheds light on the nature of the divergent sum
the moar you know

>> No.3558723

How about this for a proof?

0+1+2+n+(n+1) ect. = sum of natural numbers

When n is always positive

Positive =/=-1/12

Also fuck you

>> No.3558725

Pro tip: the notation does not mean what you think it does

>> No.3558753

Yeah, we all saw Good Will Hunting, OP. Grats.

>> No.3558762

so, if i spend the remainder of my life adding up every single motherfucking number known to man, 24/7, no breaks, with a supercomputer, i will obtain -1/12?

>> No.3558767

This thread is full of kiddies talking about something they don't understand. To make it simpler, this is what is happening in this thread right now:

8 year old: Hey guys! I found this long purple stick in my mom's closet! I think it's supposed to make you feel good or something. Something called 'sex'. But how does it work?

Other 8 year old #1: what the fuck, that's total bullshit, how DOES A STICK pleasure you? i mean it doesn't even have a computer screen on it!

Other 8 year old #2: Hey guys, look what I found! It's a book that adults look at that explains how to use a dildo! It says something about sticking it up a vagina or something.

8 year old #1: NO YOU'RE A FUCKING RETARD, THAT DOESN'T EVEN MAKE ANY GODDAMN SENSE, WHAT THE HELL ARE THOSE FUNNY POSITIONS IN THE BOOK, FUCK YOU

(OP) 8 year old: Guys, guys, I have a solution, alright, wanna hear it? I think we're supposed to stick these things... in each other's EYES.

8 year old #1: Wow, that sounds cool! I wanna go first!

OP: Okay, you ready? On a count of three, I'm going to slam this thing through your eye. Three... two...

>> No.3558779

>>3558551
>>He said that if you add up all the natural numbers, you don't get some faggy "divergent series." No sir. You get -1/12. That's right, I said -1/12. What now aspies?

that's really misleading
since that doesn't mean what we think it means

>> No.3558806

>>3558630
>divergent series
>converges to a rational number
hurr DURR

>> No.3558809
File: 16 KB, 634x571, 1313125998172.png [View same] [iqdb] [saucenao] [google]
3558809

>>3558806

>> No.3558841
File: 16 KB, 268x321, 1313214771081.jpg [View same] [iqdb] [saucenao] [google]
3558841

bow to your currynigger god

>> No.3558890

>sum of a set with positive elements closed under addition adds up to a negative fraction

sounds legit

>> No.3559005
File: 235 KB, 500x333, wheel136.png [View same] [iqdb] [saucenao] [google]
3559005

>Mfw I learned about this guy in 10th fucking grade

I think it was also this guy that wrote like hundreds of pages of proofs but no one ever knew what they were for or how they worked.

>> No.3559018

Ramanujan was a genius and OP is a hipster. End of story.

>> No.3559101

>Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a sum to infinite divergent series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
>Ramanujan summation essentially is a property of the partial sums, rather than a property of the entire sum, as it doesn't exist.
http://en.wikipedia.org/wiki/Ramanujan_summation

>> No.3559115

>implying numbers are natural.

>> No.3559125

A common anecdote about Ramanujan relates to the number 1729. Hardy arrived at Ramanujan's residence in a cab numbered 1729. Hardy commented that the number 1729 seemed to be uninteresting. Ramanujan is said to have stated on the spot that it was actually a very interesting number mathematically, being the smallest natural number representable in two different ways as a sum of two cubes:

Generalizations of this idea have created the notion of "taxicab numbers". Coincidentally, 1729 is also a Carmichael Number.

-From Wiki

>> No.3559131

>>3559125

Oh the equation was

1729 = 1^3 + 12^3 = 9^3 + 10^3

>> No.3559139

>>3558551
http://en.wikipedia.org/wiki/Regularization_(physics)
http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_·_·_· 1 + 2 + 3 + 4 + ...
http://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_·_·_· 1 + 1 + 1 + 1 + ... = -1/2 or inf
http://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_·_·_· 1 + 2 + 4 + 8 + ... = -1 or inf
http://en.wikipedia.org/wiki/1_−_2_%2B_3_−_4_%2B_·_·_· 1 − 2 + 3 − 4 + ... = 1/4
http://en.wikipedia.org/wiki/1_−_2_%2B_4_−_8_%2B_·_·_· 1 − 2 + 4 − 8 + ... =
http://en.wikipedia.org/wiki/Divergent_series
Weird stuff, but it's usually the meaning used in physics.

>> No.3559144
File: 52 KB, 480x600, 480px-Leonhard_Euler_2.jpg [View same] [iqdb] [saucenao] [google]
3559144

>>3558551
I'm sorry, the sound of pervasive reverence and veneration of my genius is making your little mathematical inanity inaudible.

>> No.3559387

9yo wife.

>> No.3561277

Mathematicians used to scoff at imaginary numbers, until it turned out they're invaluable in physics. They still haven't come around to physicists' views on so-called "divergent series" but they'll get their panties unbunched eventually. The simple fact is that 1+2+3+4+... = -1/12. It's a useful identity in physics, and no crazier than the idea that -1 has a square root.

>> No.3561417

It's actually the constant term in the asymptotic expansion (with respect to X) of the smoothed series added up to X. You happy now?

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