What does /sci/ think of the sum of infinity?

I thought i was the square root of -1. Does this mean that an infinite sum of imaginary numbers is a real one? wow

>the sum of i for i to infinity equals minus a twelfth
What did he mean by this?

>>8974415
>believe
you don't have to "believe" shit you brainlet. if you don't have the intuition you read the proof and then you try to understand it

>>8974415
It doesn't equal -1/12.

Their proof is wrong. 1 -1 + 1 -1.... does not equal 1/2

>>8974429
"i" in this case does not stand for the square root of -1.
It stands for index.
This equation is basically saying that 1+2+3+4... = -1/12

>>8974474
wrong

>>8974415
there is no such thing as a true sum of infinity. Maybe the closest thing would be a sum of infinity which is useful in the most contexts. The point is, the sum of infinity depends on the context, and essentially all ways of summing it are valid. But not all are useful. -1/12 is useful for a lot of things and is also known to have an existing representation in reality. When calculating the attraction between surfaces due to the casimir effect the riemann zeta function is used.

What the fuck is wrong with you? This is an incoherent statement as whoever made it doesn't understand the syntax.

Fucking retards, go read a calculus book.

>>8974474
that's right. 1-1+1-1...=1/2 is a common misconception, but surprisingly the correct result is 17/13.

[eqn]S = 1 - 1 + 1 -1+\dots \\
= (1-1) + (1-1)+\dots \\
= (17-17) + (17-17)+\dots\\
= 17 -(17-17) - (17-17)-\dots\\
=17 - (12-12) - (12-12)-\dots\\
= 17-(12-12+12-12+\dots)\\
=17 - 12(1-1+1-1+\dots) = 17 -12S.[/eqn]
One has [math]S = 17 - 12S[/math] and the result follows.

>>8974792
Oh you, don't even, don't you even start will this troll math shit.

I can make 1-1+1-1... equal any (real) number I want because of rearrangement theorem.

Rearrange the terms like this:

1 - 1 + 1 + 1 - 1 + 1 + 1 - 1 + 1 + 1 - ... (two steps forward one step back)

Oh look now the sum diverges to positive infinity. Notice there are the exact same number of "-1"s as there are "+1"s.

Rearrange the terms like this: (add two ones, subtract two ones, repeat)

S = 1 + 1 - 1 - 1 + 1 + 1 - 1 - 1 + 1 + 1 -.....

S = 1 + 1 - ( 1 + 1 - 1 - 1 + 1 + 1 -.....)

S = 1 + 1 - S

2S = 2

S = 1

Magic. rearrange again: (add three, subtract three)

S = 1 + 1 + 1 - 1 - 1 - 1 + 1 + 1 + 1 - 1 -1 - 1 + 1 + 1 + 1 .....

S = 1 + 1 + 1 - ( 1 + 1 + 1 - 1 - 1 - 1 + 1 + 1 + 1 - ....)

S = 1 + 1 + 1 - S

2S = 3

S = 3/2

Magic.

>>8974415
We've been over this a million times. That series is divergent. Ramanujan summation =/= standard summation.

>>8974753
What this guy said. I'm doing my thesis on the Casimir effect and there are various ways of regulating the infinite sums, all of which give the same result (atleast for simple models), the easiest being using the zeta function.

I don't really understand the proof, but since this is an actual physical effect which has been experimentally verified (Lamoreux, I think in 98), whether you agree with it or not, it's there.

>>8974415
Utterly retarded.

Assume [math]\sum_{i=1}^\infty i = -\frac{1}{12}[/math]
As we all know [math]1+1+1+...=-\frac{1}{2}[/math]
We also know that [math]1+2+3+4+...=(1)+(1+1)+(1+1+1)+(1+1+1+1)+... = 1+1+1+...=-\frac{1}{2}[/math]
Therefore [math-]\frac{1}{2}=-\frac{1}{12}[/math]
So [math]1=6[/math], a contradiction, therefore [math]\sum_{i=1}^\infty i \neq -\frac{1}{12}[/math]

>>8974415
I'm a mathematician and I think physicists are disgusting fucking plebs and should be burned.

Mathematical physics is kinda fine.

To be more elaborate, the series diverge and physicists assigned the number based on what's convenient for them. You may as well invent 'Anons Kewl Sum' assigning the series to another arbitrary value. Bonus points if you make up rules to apply AKS to other series.

>>8976504
>they invented a method to solve a problem and got counterintuitive result, therefore they're disgusting
but that's how all the maths works mate
and if you knew anything past calc I you'd know summing divergent series is not just something made up by physicists and has its place in maths

>>8974753
cs major pls go

>>8976504
I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>>8977052
anon they're called complex numbers, and numbers are an idea, not some property of the universe.

So what about an `infinite set'? Well, to begin with, you should say precisely what the term means. Okay, if you don't, at least someone should. Putting an adjective in front of a noun does not in itself make a mathematical concept. Cantor declared that an `infinite set' is a set which is not finite. Surely that is unsatisfactory, as Cantor no doubt suspected himself. It's like declaring that an `all-seeing Leprechaun' is a Leprechaun which can see everything. Or an `unstoppable mouse' is a mouse which cannot be stopped. These grammatical constructions do not create concepts, except perhaps in a literary or poetic sense. It is not clear that there are any sets that are not finite, just as it is not clear that there are any Leprechauns which can see everything, or that there are mice that cannot be stopped. Certainly in science there is no reason to suppose that `infinite sets' exist. Are there an infinite number of quarks or electrons in the universe? If physicists had to hazard a guess, I am confident the majority would say: No. But even if there were an infinite number of electrons, it is unreasonable to suppose that you can get an infinite number of them all together as a single `data object'.