1+2+3+4... = -1/12 Can someone explain this shit to a brainlet?

File: gavin.jpg (6KB, 225x225px) Image search: [Google]

6KB, 225x225px

>>9041308
Considering the Riemann Zeta function on the complex plane to be analytically continuous gives us that the output for the input of -1, which results in the addition of all natural whole integers, is analytically continuated to be -1/12

It's simple math anon. Consider being a philosopher or other brainlet subjects

>>9041323
But the rienmann zeta function is another story, still doesn't make 1+2+3+4... equal -1/12. How the fuck does that not add up to infinite?

If you can't intuitively see why it would be -1/12, then you probably shouldn't be studying mathematics. It's basic convergence. 1 + 2 is a very small part of the way to -1/12. 1 + 2 + 3 is a slightly larger part of the way, etc.

>>9041345
But you can't get negative numbers adding positive numbers, nor fractions adding whole numbers, nor a number smaller than any of those you're adding, etc...

It goes against logic.

What's even crazier is you can subtract any number from -1/12 and up with the same figure, because it's isomorphic to infinity. So -1/12 - 5 is just -1/12 and so on.

>>9041363

Not the person you're responding to, but I've heard it described as like a gravitational singularity but in the number space. If you imagine an infinite number line with nonfinite curvature, eventually it will "bottom out" so to speak (I'm using heavy analogies here) at some arbitrary point near zero. That just so happens to be -1/12 according to proofs.

>>9041335
It's a divergent series, it does not sum to -1/12.
The zeta function is not "another story", it is exactly the -1/12 story. When a function is analytically continued from its natural domain the results don't necessarily make any intuitive sense.

>>9041308

It's trivial

https://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_⋯

https://en.wikipedia.org/wiki/Riemann_zeta_function

>>9041323
>Consider being a philosopher or other brainlet subjects

At least OP has the same level of Intelligence as a PhD (in Humanities)

File: 1500148398721s.jpg (7KB, 220x229px) Image search: [Google]

7KB, 220x229px

>>9041308
It's a lie

Ramanujan just played around with series instead of adding everything up

>>9041404
>At least OP has the same level of Intelligence as a PhD (in Humanities)
Top kek cause I'm OP and I actually have a PhD in Humanities, math is just a hobby for me.

[math]\zeta(s)\neq\sum\frac{1}{n^s} \text{for} Re(s)\leq 1 [/math]

>>9041308
You're just using a different summation method, namely zeta function regularization or Ramanujan summation. It's essentially a semantics problem, you asked why the infinite series 1 + 2 + 3 + ... converges, but it doesn't. Using the traditional series summation method the series is divergent. It may be the same plus symbol but it means different things from context.

I guess a kind of crappy analogy would be momentum in physics. If you just say momentum when talking about the mechanical momentum it may lead to confusions if someone is talking about the canonical momentum.

Convergent means a you can approximate the value of a series by taking partial sums of the series.
Divergent means you can't approximate it, but methods that assign correct values to convergent series may also be used to assign values to divergent series.

>>9041308
Yes I can. But only to brainlets.

>>9041363
Because you are not adding 1 + 2 + 3 + 4

You are addings soemthign else, iirc they are called sets or some weird shit taht uses sums, they are not numbers

it's basically conceptual. takes the sum of a set defined as n*(n+1) / 2 and you end up with -1/12. You are not adding up numbers, you are doing some weird abstract shit.

Thanks god I'm an engineer, we only learn shit that can actually be measured.