Did I make a mistake? Or is analytic continuation just a retarded meme?

Did I make a mistake? Or is analytic continuation just a retarded meme?

Other urls found in this thread:

math.stackexchange.com/questions/157045/explanation-of-zeta-function-and-why-1234-1-12
math.stackexchange.com/questions/39802/why-does-123-cdots-frac112
terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/
twitter.com/SFWRedditVideos

1+2+3+... != -1/12 no matter how many times you watch the numberphile video

That's not even my question

Your mistake was at Σn = -1/12 and the guy who replied to you was on point.

Oh and at Σn^3=ζ(-3)
Τhat's not what ζ(-3) is.

what is it then?
is the riemann zeta not the summation of the reciprocal of all natural numbers raised to the power of s (in this case -3)?

I worded really poorly, but you know what i mean

It is not. The zeta function is defined as Σ1/n^s for s with Re(s)>1 and then, for the rest of the complex plane, you take the (unique) entire function which agrees with Σ1/n^s for s with Re(s)>1.

For Re(s)

>!= as "not equal"
Stay pleb Veeky Forums

is it not true though that
1 + 2 + 3 + 4 + ...
has an "assigned value" of -1/12 because that is where the analytic continuation of the riemann zeta function lands at -1/12 for s = -1, even it doesn't literally equal it?
And if so, does my problem not remain intact in the sense that multiple values are assigned to the same thing?
I don't know much about this form of math (I dropped out of high school and never studied maths at a higher level) so forgive me if I come across as a complete moron.

>is it not true though that
1 + 2 + 3 + 4 + ...
Yes, it is true. Since that continuation is unique(it's a bit hard to prove that, but it is true), you can say that Σn corresponds to -1/12. But it is not equal to it and you can't do operations with -1/12 and get truths about Σn. Your picture in the OP shows that.

>forgive me if I come across as a complete moron.
You definitely don't sound like a moron. A moron wouldn't ask such questions.

To be clear you can use -1/12 to get info about the behavor of Σn, but I haven't studied about that. I remember hearing that it was being used in string theory or something.

You can also take a look at math.stackexchange.com

math.stackexchange.com/questions/157045/explanation-of-zeta-function-and-why-1234-1-12

math.stackexchange.com/questions/39802/why-does-123-cdots-frac112

Take a look here as well:

terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

Let's do the following proof by contradiction:

>Assume that one can assign [math]\sum{n^s}[/math] the value of [math]\zeta(s)]/math] for Re(s) < 1
>(a) 1 + 2 + 3 ... = -1/12
>(b) 1 + 1 + 1 ... = -1/2
>Subtracting (b) from (a) yields 0 + 1 + 2 + 3 ... = -1/12 - (-1/2)
>0 + 1 + 2 + 3 ... is still 1 + 2 + 3 ...
>5/12 = -1/12

See something wrong there?

> != isn't 'not equal'

>Did I make a mistake?
Yes.
>Or is analytic continuation just a retarded meme?
Yes.

Terry Tao explains the values of zeta at negative values as the constant value appearing in the
(not necessarily convergent) asymptotic expansion using a sufficiently decaying cutoff function.

terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

Shit, repost of
My bad
:(
We eat the same food

He should have XOR'd
OP is sloppy OR he believes the Law of excluded middle.

Cs fag go home