Why is -1/12 wrong?

[Anonymous No.9191720]

Why is the "sum of the naturals = -1/12" such a meme?

Are people saying it's wrong? It felt weird intuitively, but the proof seems OK to me

https://www.youtube.com/watch?v=w-I6XTVZXww

What's wrong with this?

[Anonymous No.9191732]

There's nothing wrong with it. Just shows infinity is bullshit.

[Anonymous No.9191736]

>>9191720
1-1+1-1+1... is not equal to a half (or one or zero). The sum never converges, and so you cannot say that it has a value.
You can only give a value to an infinite sum if it converges.

[Anonymous No.9191737]

>>9191736
>>9191720
Yeah that's what I was thinking...

[Anonymous No.9191739]

>>9191736
>>9191737
It's like saying sin(infinity) = 0, right? or sin(x) as x approaches inf is 0, but it's undefined since it doesn't converge

[Anonymous No.9191743]

>>9191732
>>9191720
It is kind of "wrong" in the sense that they shouldn't have used an "=" symbol. There is no real "equality" between the left and right sides of that equation.

The infinite sum on the left can be represented by [math]-{\frac{1}{12}}[/math] in some domains... like analytic continuation. And that can even be useful in solving some other problems.

But no mathematician would (or should) ever claim that if you add up all the positive integers, the sum "equals" [math]-{\frac{1}{12}}[/math].

[Anonymous No.9191745]

>>9191743
>>9191720
Also, OP, your image is wrong. The subscript should be "1" and not "i." I guess zero would be fine, too.

[Anonymous No.9191771]

You should have kept this in the other thread.

The sum is not equal to -1/12. There is a function which when analytically continued to the negative real axis has a value of -1/12 at argument of -1. This function is only equal to a sum of the form in the picture when the argument has real value greater than 1.

[Anonymous No.9191798]

He started by stating that s=1/2 then went on to say s=-1/12.....