[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 92 KB, 590x337, infinite.jpg [View same] [iqdb] [saucenao] [google]
7505089 No.7505089 [Reply] [Original]

What do you think about this guys?

Is this possible?

which it is proof for this?

>> No.7505098

>>7505089
You simply have to triple integrate the sum of n while taking into account the quantum skeleton effect.

>> No.7505102

>>7505098
/saged

>> No.7505119
File: 401 KB, 450x253, smug.gif [View same] [iqdb] [saucenao] [google]
7505119

>>7505089

>which it is proof for this?
>which it is proof
>it is proof
>is proof

Here it is proof for this:

Analytic continuation of the zeta function gives zeta(-1) = - 1/12.

If you want to know more pick up a book on complex analysis.

e.g. Alfhors

You should also know that this series diverges to +inf in the classical sense of convergence. i.e. 1 + 2 + ... = -1/12 should not be understood in the way 1+1/4+1/9+ ... = (pi^2)/6 is.

>> No.7505171

We have 1 - 1 + 1 - 1 + ... = -1/2

So 1 - 2 + 3 - 4 + ... = 1/4

But then (1 + 2 + 3 + 4 + ...) - 2 (2 + 4 + 6 + 8 + ...) = 1/4. So (1 + 2 + 3 + 4 + ...) = -1/12.

>> No.7505344

>>7505089
Look up zeta function on wikipedia

>> No.7505368

>>7505119
is there any proof that the zeta function is functional in this way?

>> No.7505407
File: 81 KB, 500x500, 0015 - rUHFbjL.jpg [View same] [iqdb] [saucenao] [google]
7505407

>>7505368
>is there any proof that the zeta function is functional in this way?

the zeta function is given by (for Re(s)>1):

zeta(s) = 1^-s + 2^-s + 3^-s + ...

It's the only 'nice' function with this property. So that gives us some justification for saying zeta(-1) = 1 + 2 + 3 + ... .

>> No.7505420

>>7505089
Maybe I'm dumb but isn't the image top line n! Where n is infinity

>> No.7505423

>>7505420
n! is the product 1*2*...*n. This is the sum 1+2+3+... .

>> No.7505425

>>7505423
Oh. Right. I am dumb

>> No.7505443

>>7505420
The zeta-regularised factorial at infinity is <span class="math">1 \cdot 2 \cdot 3 \cdot 4 \cdots = \sqrt{2 \pi}[/spoiler] if you're curious.

Also the zeta-regularised infinite primorial is <span class="math">2 \cdot 3 \cdot 5 \cdot 7 \cdots = 4 \pi^2 [/spoiler].

>> No.7505450
File: 88 KB, 1044x520, math example.png [View same] [iqdb] [saucenao] [google]
7505450

>> No.7505520

>>7505344
better yet, look at where -1/12 is in this image

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF#/media/File:Sum1234Summary.svg