If there is an infinite amount of natural numbers, and the sum of all of them = -1/12, does that mean the sum of all primes also = -1/12 since there is an infinite amount of them?
>>8191395
yea man
No.
Yes yes well done. However, what is the sum of all non-numbers?
>>8191395
>assuming that there's an infinite amount of numbers
Didn't you know? 10^200 is the biggest number
By that logic, the sum of all even integers would be -1/12 (not -1/6)
>>8192011
I don't like it. I don't like any of i one bit.
I demand an explanation for why the system generating these results is of any utility, and why it should be treated as valid. It's used heavily in physics, but that just masks something else going on. Gibberish should be torn apart.
Better yet, Ramanujan shouldn't have died off so early.
>>8191395
The sum isn't -1/12. This sum is infinite
>>8192024
I don't like it either, but there seems to be something to it (maybe a new way to classify infinities)
>>8192024
>I demand an explanation for why the system generating these results is of any utility
What does that mean?
Can you give an example for an explanation clarifying why a system generating some results is of utility?
What's the """reason""" the results that calculus, differential equations and so on generates is of utility.
I'd say either it applies and is used, or it's not.
>>8192061
I mean why should a system be able to just sit there and sum all positive integers, and arrive at a negative fraction, and ave people just leave it to get away with that?
What's its problem? Does it even have one?
>>8192086
>Actually
Enlighten us please
wow this infinite sum mathematics looks really cool. let me have a go too:
x = 1 + 1 + 1 + 1 +.....
x - x = 1 + (1-1) + (1-1) + ...
0 = 0... or 1 or 2 or 3 or 5
who knows really lets just start from scratch
>>8192204
Cool, yes, but you're doing it wrong
>>8192075
I don't see your problem.
If it helps you anything (having -1/12 pop up in classical analysis )
[math] 0+1+2+3+4+...= \lim_{z \to 1} \sum_{n=0}^\infty n\,z^n = \lim_{z \to 1} z\dfrac{d}{dz}\sum_{n=0}^\infty z^n= \lim_{z \to 1} z\dfrac{d}{dz} \dfrac{1}{1-z} = \lim_{z \to 1} \dfrac{z}{(z-1)^2} [/math]
where sadly the limit z to 1 of the the function doesn't exists (as it shouldn't).
But if you add the counter term [math] -\dfrac{1}{\log(z)^2} [/math] (the derivative of 1/log(z)) then (even though both have a pole at z=1 individually) the limit of the sum equals -1/12, or -0.08333
>>8192142
A picture is worth a thousand words
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF#/media/File:Sum1234Summary.svg
>>8192297
>(the derivative of 1/log(z))
I don't see how this function holds any significance to the matter at hand.
the sum of all natural numbers is infinite, not -1/12. This is only true in ramanamanama's zeta function which doesnt apply to basic sums
>>8192471
Wonder why Ramanujan summation fits in physics equations better than "basic" summation.
>>8192485
This is a good question, do you have an answer? I study math, not physics so I don't know. If I had to guess it would be that physics equations don't work well with infinity being involved
>>8192498
Physics doesn't seem to care why, but I would think the mathematicians would be ahead of the physicists on practical understanding of the behavior of infinite sums vs Ramanujan sums.
