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?
If there is an infinite amount of natural numbers, and the sum of all of them = -1/12...
Noah Taylor
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Ethan Gray
yea man
Ryder Peterson
No.
Jackson Wood
Yes yes well done. However, what is the sum of all non-numbers?
Andrew Price
>assuming that there's an infinite amount of numbers
Didn't you know? 10^200 is the biggest number
Grayson Wood
By that logic, the sum of all even integers would be -1/12 (not -1/6)
Adrian Diaz
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.
David Nguyen
The sum isn't -1/12. This sum is infinite
Noah Rodriguez
I don't like it either, but there seems to be something to it (maybe a new way to classify infinities)
Ethan Cook
>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.
Ethan Murphy
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?
Leo Cook
>If there is an infinite amount of natural numbers, and the sum of all of them = -1/12,
mfw people actually got memed into believing this was the actual sum of natty numbers and not just under zeta function
Lincoln Thompson
>Actually
Enlighten us please
Grayson Davis
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
Jace Hall
Cool, yes, but you're doing it wrong
Kevin Diaz
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
Sebastian Jenkins
A picture is worth a thousand words
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Tyler Evans
>(the derivative of 1/log(z))
I don't see how this function holds any significance to the matter at hand.
Cameron Young
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
Michael Stewart
Wonder why Ramanujan summation fits in physics equations better than "basic" summation.
Samuel Russell
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
Camden Allen
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.