Analysis

analytic number theory

Euclidean elements

How to Convince Your Wife to Cuck You: The Basics

>>9061078
I'm always annoyed when people define the Zeta function like that, it isn't the complete definition of what it is.

File: 1491923073860.png (137KB, 482x651px) Image search: [Google]

137KB, 482x651px

>>9061088
>I'm always annoyed when people define the Zeta function like that

File: Matt.png (330KB, 702x1056px) Image search: [Google]

330KB, 702x1056px

>>9061088

>>9061091
>>9061093
1+2+3 .. = -1/12 amirite

>>9061097
absolutely

>>9061099
Because I don't have the time to actually add it or see where it is going so you can just say it is anything right?

>>9061078
analysis, as you said. try Tao's Analysis I for a great introduction

>>9061151
Thanks for a legit answer!

>>9061078
Anything Fourier series.
Basically it is an infinite dimensional vector space where the basis vectors are the functions sin's and cos's of all integer frequencies.

https://en.wikipedia.org/wiki/Parseval%27s_theorem

Dirichlet kernel and Fejer kernel for convergence criteria

Hell give Euler-Maclaurin formula a try

>>9061091
The subtleties of complex exponents and branch cuts...

File: NegativeZeta.gif (10KB, 604x658px) Image search: [Google]

10KB, 604x658px

>>9061097
Yes

>>9061104
You are ok with 0.33333...=1/3
Are you ok with ...99999.0=-1?

https://en.wikipedia.org/wiki/Two%27s_complement

For inspiration

File: 6a02af6431c61012d43eb5f3b07ad5b0_400x400.jpg (30KB, 279x400px) Image search: [Google]

30KB, 279x400px

>>9061278
>infinite dimensional vector space
>basis
No such thing.

>>9061298
https://en.wikipedia.org/wiki/Hilbert_space

SMD

>>9061287
So? That still isn't proof that infinity = -1/12

>>9061306
>SMD
Shaking my dick?

File: Riemann_sphere.png (39KB, 225x180px) Image search: [Google]

39KB, 225x180px

>>9061307
Know the context.
Learn some Complex Analysis

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

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

Sums get to infinity then wrap around (kind of like how the graph of y=1/x "jumps" from negative infinity to positive infinity)

>>9061310
See My Disproof

>>9061337
>Sums get to infinity then wrap around (kind of like how the graph of y=1/x "jumps" from negative infinity to positive infinity)

I know all that already and none of it justifies saying that infinity is -1/12

>>9061347
Nature is ok with it. I don't think you understand infinity.

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

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

>>9061350
>I don't think you understand infinity.
>I don't think
Convincing yourself in your head that 1+2+3... = -1/12 is pretty much the definition of not thinking, wouldn't you say?

>>9061347
There are other absolute values used for convergence criteria that do not resemble your intuitive notion of distance.

https://en.wikipedia.org/wiki/P-adic_order#.7F.27.22.60UNIQ--postMath-00000028-QINU.60.22.27.7F-adic_absolute_value

https://en.wikipedia.org/wiki/Ostrowski%27s_theorem

>>9061380
You're just trying to throw sand in my eyes at this point.

>>9061383
It's already there

>>9061385
You've done nothing but show me things I already know that don't prove infinity = -1/12

"Morally the truth" and "literally the truth" are two separate things, the former only means that you in your mind somehow got it twisted enough to make it seem as though something as absurd as infinity = -1/12 is true. [math]\sum_{x\to\infty}x=\infty[/math] no matter how you want to look at it.

If you really want to keep deluding yourself then go ahead, see how well it works out for you in life.

>>9061403
>If you really want to keep deluding yourself then go ahead, see how well it works out for you in life.
Likewise

>>9061307
>proof that infinity = -1/12
I think you are misunderstanding the idea. The infinite series 1+2+... doesn't equal anything at all. We are assigning values to it in a purely formal way, and there are many ways to assign them. One way is by using the limit of partial sums. For any number we can add up a finite number of terms to exceed it. Another way is by analytic continuation of the zeta function.

>>9061298
Are you retarded? All vector spaces have a basis (Lemma of Zorn or AC).
No infinite dim. Banachspace has a countable basis though.

>>9061306
Idiot. An orthogonal basis is NOT a basis.

File: 1499263174435.jpg (31KB, 480x480px) Image search: [Google]

31KB, 480x480px

>>9061829
>he believes in the axiom of choice
you know how I know you're an undergrad?

Analysis and Combinatorics

Not quite series in the traditional sense but generating functions deal with summations.

Also analysis in general of course.